The value of x is 2.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The point as far as she can tell are (3,5) and (x,10).
Slope is -5.
-5=10-5/x-3
-5=5/x-3
-5(x-3)=5
Apply distributive property
-5x+15=5
Substitute 15 from both sides
-5x=-10
Divide both sides by 5
x=2
Hence, the value of x is 2.
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when multiplying matrices, multiply the elements in each of the first matrix times the corresponding elements in each. is it true?
False, every component of the matrix is multiplied by the same amount when you multiply a matrix by a number. A new matrix is created by this operation; it is known as a scalar multiple.
A rectangular matrix is a grouping of numbers in rows and columns. A matrix element/entry is the term used to describe each number in the matrix. The combination of a real number and a matrix is referred to as scalar multiplication.
Each entry/element of the matrix is multiplied by the specified scalar in scalar multiplication. Comparatively, matrix multiplication describes the result of two matrices. This operation is totally different. We can't just multiply the corresponding entries in two matrices to multiply them.
The first matrix must have exactly as many columns as the second matrix has rows in order to perform matrix multiplication. The resulting matrix has the same number of columns and rows as the second matrix, and its number of columns matches the number of rows in the first matrix.
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what is p value significance
In statistics, p-value significance is the measure of the strength of evidence against the null hypothesis.
P-value significance is used to determine whether or not a result is statistically significant. The p-value is the probability of obtaining the observed results or more extreme results if the null hypothesis is true. If the p-value is below the chosen significance level, usually 0.05, the null hypothesis is rejected, indicating that the results are statistically significant.
This means that the observed data is unlikely to have occurred by chance alone and that there is strong evidence to support the alternative hypothesis. P-value significance is an essential concept in hypothesis testing, and it is widely used in scientific research, medical trials, and other statistical analyses.
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What is the conversion of 2000 pounds to dollars ?
The conversion of 2000 pound sterling to dollars is 2,740 US dollars.
The conversion of 2000 pounds sterling to dollars depends on the current exchange rate between the two currencies.
The exchange rate was approximately 1.37 US dollars per 1 British pound.
Using this exchange rate, we can convert 2000 pounds sterling to US dollars as follows:
2000 pounds * 1.37 dollars/pound = 2,740 US dollars
Therefore, 2000 pounds sterling is equivalent to approximately 2,740 US dollars using the exchange rate mentioned above. However, please note that exchange rates can fluctuate over time, so the exact conversion may be different depending on the current exchange rate.
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Correct Question :
What is the conversion of 2000 pound sterling to dollars ?
Show the ratios are equivalent by simplifying any 4 of them.
The ratios are equivalent by simplifying is shown below.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
We have first ratio 3:1
and, second 6:2 on simplifying we get 3:1.
and, third 9: 3 on simplifying we get 3:1.
and, Fourth 12:4 on simplifying we get 3:1.
So, all the ratio gave same value on Simplification which shows the ratios are Equivalent.
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renata is a 5-year-old girl from a poor family in the united states, who is about to enter kindergarten. according to recent statistics, the chances of renata being ready to complete kindergarten tasks when she enters school are about:
The chances of Renata being ready to complete kindergarten tasks when she enters school are about 1/2. The solution has been obtained by using the concept of probability.
What is probability?
To calculate the chance of an event, use the mathematical notion of probability. It only enables us to estimate the likelihood that an event will take place. On a scale of 0 to 1, where 0 represents impossible and 1 represents a certain event.
We are given that Renata is a 5-year-old girl from a poor family in the united states, who is about to enter kindergarten.
The chances of Renata being ready to complete kindergarten tasks when she enters school are about 1/2 because it is not necessary that she will be able to do all the tasks. She might be able to do and she might not be able to do.
So, there are equal chances of both.
Hence, chances of Renata being ready to complete kindergarten tasks are 1/2.
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Find the perimeter of the composite heart shape, round to two decimal places. pls help
Answer:
18.00 cm
Step-by-step explanation:
This composite heart shape consists of two semi-circles and a rectangle.
[tex]r_{ssc}[/tex] = radius of small semi-circle
= [tex]\frac{3 cm}{2}[/tex] = 1.5 cm
[tex]r_{bsc}[/tex] = radius of big semi-circle
= [tex]\frac{4 cm}{2}[/tex] = 2 cm
Perimeter of this composite shape
= Perimeter of big semi-circle + Perimeter of small semi-circle + 2 outer sides of the rectangle
= [tex](\frac{2}{2} \pi r_{bsc} + \frac{2}{2} \pi r_{ssc} + 3 + 4)[/tex] cm
= [tex](\pi r_{bsc} + \pi r_{ssc} + 3 + 4)[/tex] cm
= [tex][\pi (2) + \pi (1.5) + 3 + 4][/tex] cm
= [tex](2\pi + 1.5\pi + 7)[/tex] cm
= [tex](3.5\pi + 7)[/tex] cm
= 17.995 cm
= 18.00 cm (Rounded to two decimal places)
Please help me ASAP! Thank you! 15 points
Simon and his friends have 27 pieces of candy. They split them up evenly and each person get 9 pieces. How many people are there? Select the correct equation and solve for p.
A. 27 = 9p; p = 3
B. 9 + p = 27; p = 18
C. p/27 = 9; p = 3
D. 9 = 27 - p; p = 18
Answer:
[tex] \sf \: a) \: 27 = 9p \: ; p = 3[/tex]
Step-by-step explanation:
Given information,
→ Simon have 27 pieces of candy.
→ Each person will get 9 pieces.
Now we have to,
→ Find the required equation.
The equation will be,
→ 27 = 9p
→ 9p = 27
=> As each person (p) gets 9 pieces.
Then the value of p will be,
→ 9p = 27
→ p = 27 ÷ 9
→ [ p = 3 ]
Hence, option (a) is correct.
2
Simplify the expression
(1 point)
The simplified form of the expression x² - 8x +16 is (x - 8)²
Expressions are mathematical statements that involve operations, such as addition, subtraction, multiplication, and division. In this problem, we are given the expression x² - 8x + 16 and asked to simplify it.
The expression can be simplified by using factoring techniques. We can factor the expression as (x - 8)(x - 8), which can be further simplified as (x - 8)2. The simplified expression is (x - 8)²
Therefore, the simplified expression for x² - 8x + 16 is (x - 8)². This shows that the expression is a perfect square, which can be written as (x - 8)², where (x - 8) is the square root of the expression
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Complete Question:
Simplify the expression x² - 8x + 16
Find the common ratio of the geometric sequence -10, 20, -40,
The common ratio of the geometric sequence -10, 20, -40 is -2.A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a fixed number called the common ratio.
To find the common ratio of the sequence -10, 20, -40, we can divide each term by the previous term.
The second term divided by the first term gives:
20 / (-10) = -2
The third term divided by the second term gives:
(-40) / 20 = -2
We can see that the quotient is the same in both cases, which means that the common ratio of the sequence is -2.
This tells us that to find the next term in the sequence, we multiply the previous term by -2. For example, to find the fourth term, we would multiply -40 by -2 to get 80, which would be the next term in the sequence.
In summary, the common ratio of the geometric sequence -10, 20, -40 is -2.
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what is 1.86 m in feet?
The value of given 1.86 meters after converting it into feet is equal to 6.1024 feet.
Meter is the unit which is used to measure length.Feet is the unit which is also used to measure length.Both are used to measure length we can convert meter to feet.1 meter is equal to 3.28084 feet
⇒ 1.86 meters = ( 1.86 ) × ( 3.28084 ) feet
⇒ 1.86 meters = 6.1023624 feet
Round off the value upto four decimal places we get,
⇒ 1.86 meters = 6.1024 feet
Therefore, the unit of 1.77 meters after converted to feet the value is equal to 6.1024 feet ( approximately ) .
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PLEASE HELP ME?!!
Explain how to factor a polynomial
completely. Pick two of the following
polynomials to help explain how to
completely factor.
-
x5 – x³
3x² – 75
2
3x5y + 4x¹y - 5x²y
x³ 125
x3
• X
X3
Be sure to reference GCF, Difference of
Squares, Sum of Cubes, or Difference
of Cubes in your answers.
Answer:
Factoring a polynomial means breaking it down into simpler parts that can be multiplied together to get the original polynomial. To factor a polynomial completely, we want to find all of its factors, including any that are in the form of a constant, a variable, or a combination of both.
Let's take a look at how to factor two of the given polynomials.
x^5 - x^3
We can factor out the greatest common factor (GCF) of x^3 to get:
x^5 - x^3 = x^3(x^2 - 1)
Now, we have a difference of squares, which we can factor using the formula:
a^2 - b^2 = (a + b)(a - b)
In this case, a = x and b = 1, so we get:
x^5 - x^3 = x^3(x + 1)(x - 1)
Therefore, the polynomial x^5 - x^3 can be completely factored as x^3(x + 1)(x - 1).
3x^2 - 75
We can factor out the GCF of 3 to get:
3x^2 - 75 = 3(x^2 - 25)
Now, we have a difference of squares, which we can factor as:
a^2 - b^2 = (a + b)(a - b)
In this case, a = x and b = 5, so we get:
3x^2 - 75 = 3(x + 5)(x - 5)
Therefore, the polynomial 3x^2 - 75 can be completely factored as 3(x + 5)(x - 5).
In general, to factor a polynomial completely, we should first look for any common factors that can be factored out using the GCF. Then, we can look for special patterns, such as differences of squares, sums or differences of cubes, or quadratic trinomials that can be factored using the quadratic formula or by factoring the sum or difference of two perfect squares. Finally, we can use trial and error or other methods to find any remaining factors that are not immediately obvious.
If you could label my answer brainliest, that would be awesome!
- Dante
Rhonda claimed that 8th graders performed better than 7th graders on the state English test.
Complete each of the 2 activities for this Task.
Rhonda recorded a random sample for the state English test scores of 40
seventh graders and 40 eighth graders. A score of 4 is the highest score
and a score of 0 is the lowest score.
Random Sample of 7th and 8th Grade
State English Test Scores
Score 7th Graders
4
3
N
1
0
8
9
18
5
0
8th Graders
3
19
10
7
1
Activity 1 of 2
Activity A: Find two measures of center, the mode and the
median to justify Rhonda's claim that 8th graders
performed better than 7th graders on the state English test.
The 7th graders mode Choose...
The 7th graders median Choose...
The 8th graders mode Choose...
Rhonda's claim that 8th graders performed better than 7th graders on the state English test seems to be supported, as the median and mode for the 8th graders are both higher than those for the 7th graders.
How did we arrive at this assertion?The 7th graders mode: 0 (since it appears twice in the sample)
The 7th graders median: 3.5 (since the scores are already sorted, the median is the average of the two middle scores, which are 3 and 4)
The 8th graders mode: 3 (since it appears twice in the sample)
The 8th graders median: 8.5 (since the scores are already sorted, the median is the average of the two middle scores, which are 7 and 10)
Based on these measures of center, Rhonda's claim that 8th graders performed better than 7th graders on the state English test seems to be supported, as the median and mode for the 8th graders are both higher than those for the 7th graders.
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Suppose you are driving. You notice that after driving for 4 hours, you are 215 miles from Seattle. You continue driving, and calculate that after driving 8 hours you are 415 miles from Seattle. What is your rate?
Your rate is 52.5 miles per hour, calculated by dividing the total distance traveled (200 miles) by the total time taken (4 hours).
To calculate this, take the total distance traveled (415 miles) and subtract the distance from Seattle at the start of the journey (215 miles). This gives you the total distance traveled, which is then divided by the total time taken (8 hours), giving you a rate of 52.5 miles per hour.
415-215/8=52.5To better understand this concept, imagine driving from Seattle to Los Angeles. You know that Los Angeles is 800 miles from Seattle, and if you drive for 16 hours, you will reach your destination. In this case, your rate would be
800/16 = 50 miles per hour.The same principle applies here, which is why you can use the same formula to calculate your rate.
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What is Statement 3.
Given: P is the midpoint of TQ and RS.
Prove: ATPR AQPS
X
Proof:
Statements
1. P is the midpoint of TQ and RS.
2. TP QP, RP = SP
3.
4. ATPR AQPS
O ZPTR
ZPQS
O ZPSQ ZPRT
OZSPQ LRPT
R
Reasons
1. Given
2.
3. Vertical Angles Theorem
4.
The statements required for the prove are given in the explanation.
What are vertical angle?Vertical angles are two opposite angles which have equal values because they are formed by two straight lines intersecting at a point.
And a midpoint is a point which divides a line segment into two equal parts.
The required statements to prove that ΔTPR ≅ΔQPS are given below;
STATEMENT REASON
1. P is the midpoint of TQ and RS Given
2. TP = QP, RP = SP Definition of midpoint
3. <SPQ ≅ <RPT Vertical angle theorem
4. ΔTPR ≅ΔQPS Side-Angle-Side theorem
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i need help with part a part b part c
Answer:
Step-by-step explanation: I'm not gonna give you the answer but i will explain what you need to do. First you need to draw a bar diagram and then you need to put the number equally. But first in part A is an easy question you only need to explain or tell the steps that you will do to solve the problem. For part C you only need to tell the answer but it says how how many got to fill equally so that means that there are gonna be equal number and an not so equal number. I hope this help you with your answer
Average health premiums have been increasing at a rate of 5% per year. If an average familys premiums are $11,430 this year, what will they be in 2 years
The compound interest of average family's health premiums will be approximately $12,593.25 in 2 years.
What is compound interest?
Compound interest is interest that is calculated not only on the initial principal but also on the accumulated interest of previous periods. This means that the interest earned each period is added to the principal, and then the interest is calculated on the new, higher principal for the next period. In other words, it is interest on interest. Compound interest can be contrasted with simple interest, which is calculated only on the principal amount. Compound interest can lead to significant growth in investment or debt over time, depending on the interest rate and the length of time.
Given by the question:
To solve the problem, we need to use the formula for compound interest:
[tex]A = P(1 + r)^n[/tex]
where A is the final amount, P is the initial amount, r is the annual interest rate as a decimal, and n is the number of years.
In this case, the initial amount is $11,430, the annual interest rate is 5% or 0.05, and we want to find the final amount in 2 years. So we have:
[tex]A = 11,430(1 + 0.05)^2[/tex]
[tex]A = 11,430(1.1025)[/tex]
[tex]A = 12,593.25[/tex]
Therefore, the average family's health premiums will be approximately $12,593.25 in 2 years.
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What is the conversion of 30 celsius to fahrenheit ?
The conversion value of Celsius to Fahrenheit for the value 30 Celsius is equal to 86 Fahrenheit.
Standard units used for measuring the temperature is named as Celsius and Fahrenheit.Relation to convert the temperature from Celsius to Fahrenheit is equal to :
°F = 9 /5 ( ° C ) + 32.
Convert 30 Celsius to Fahrenheit by substituting the value in the formula :
= 9 /5 ( 30° ) + 32
= 9 (6° ) + 32
= 54° + 32
= 86°F
Therefore, the converted values for the 30Celsius to Fahrenheit is given by 86 Fahrenheit.
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Question 10 (4 points)
The following statements describe triangles ABC and PQR-
For A ABC AC-2, AB-4, and BC= 5.
For A POR: QR-7.5, PR-3, and PQ-6.
Which statement explains why A ABC and A POR are either similar or not similar?
AABC and
A
B.
C.
D.
AABC and
AABC and
4430 and
APQR
APQR
APQR
APQR
are not similar because AC
QR
are similar because c PQ
PR
AB
=
#
are similar because AB BC
PQ
QR
=
are similar because AC BC
PR
QR
=
AB
PR
=
BC
QR
AB.
PQ
Answer:
aabc
Step-by-step explanation:
Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = €* and the line * = 8 about the line x = 8.
The volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8 is approximately 1483.6 cubic units.
To find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8, we can use the method of cylindrical shells.
To find the volume of the solid, we need to integrate the area of each cylindrical shell over the height of the solid. Let r be the radius of a cylindrical shell at height y, and let h be the thickness of the shell. Then the volume of the shell is given by:
dV = 2πrh × h
where the factor of 2 comes from the fact that there are two cylindrical shells (one on either side of the line x = 8).
We can express r and h in terms of y:
r = 8 - y
h = e^8 - e^-x
Substituting these expressions into the formula for dV and integrating from y = 0 to y = 1, we get,
V = ∫(0 to 1) 2π(8 - y)(e^8 - e^-x) dy
= 2π ∫(0 to 1) (8e^8 - 8e^-x - ye^8 + ye^-x) dy
= 2π [8e^8 - 8e^-1 - (1/2)e^8 + (1/2)e^-1]
= 2π [15e^8 - 4e^-1]
≈ 1483.6 cubic units
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The given question is incomplete, the complete question is:
Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8.
The ratio of the sides of two similar is 2/3. The area of the smaller triangle is 36cm. Find the area of the larger triangle?
Answer:
[tex]\text{Area of larger $\triangle$} = 81 \:cm^2[/tex]
Step-by-step explanation:
Given.
Ratio of corresponding sides of two similar triangles = 2:3 or [tex]\dfrac{2}{3}[/tex]
Area of smaller triangle = 36 cm²
By the property of area of two similar triangle,
Ratio of area of both triangles = (Ratio of their corresponding sides)²
[tex]\dfrac{\text{Area of smaller $\triangle$ }}{\text{Area of larger $\triangle$ }} = \left(\dfrac{2}{3}\right)^2}[/tex]
[tex]\dfrac{36}{{\text{Area of larger $\triangle$ }}} = \dfrac{4}{9}[/tex]
Cross-multiplying we get
[tex]36 \times \dfrac{9}{4} = \text{Area of larger $\triangle$}\\\\81 = \text{Area of larger $\triangle$}\\\\\text{Area of larger $\triangle$} = 81 \:cm^2[/tex]
The Banks family would like to borrow $120,000 to purchase a home. They qualified for an annual interest of 4.8%.
Algebraically determine the fewest number of whole years the Banks family would need to include in the mortgage
agreement in order to have a monthly payment of no more than $720.
The fewest number of whole years the Banks family would need to include in the mortgage agreement in order to have a monthly payment of no more than $720 is 25 years.
How can we have a monthly payment of no more than $720Let's denote the number of years by y. Then the total number of monthly payments will be 12y.
The formula to calculate the monthly payment for a mortgage loan is:
M = P * (r/12) * (1 + r/12)^(12y) / ((1 + r/12)^(12y) - 1)
where:
M = monthly payment
P = principal (the amount borrowed)
r = annual interest rate
Plugging in the given values, we get:
720 = 120000 * (0.048/12) * (1 + 0.048/12)^(12y) / ((1 + 0.048/12)^(12y) - 1)
To solve for y, we can use trial and error or a numerical solver. Using trial and error, we can start with a few values of y and check if the monthly payment is less than or equal to $720.
Trying y = 20, we get:
720 = 120000 * (0.048/12) * (1 + 0.048/12)^(1220) / ((1 + 0.048/12)^(1220) - 1)
This results in a monthly payment of $753.81, which is higher than $720.
Trying y = 25, we get:
720 = 120000 * (0.048/12) * (1 + 0.048/12)^(1225) / ((1 + 0.048/12)^(1225) - 1)
This results in a monthly payment of $715.48, which is lower than $720.
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What are the possible values of x and y for two distinct points, (5, –2) and (x, y), to represent a function?
The value of x can be
.
The value of y can be
.
Answer:
The value of x can be 10
The value of y can be -4
Step-by-step explanation:
Assume the function is linear of the form
y = mx
When x = 5, y = -2
Simply multiply x by 2 and equivalently multiply -2 by 2
x = 5 x 2= 10
y = -2 x 2 = -4
What are the dimensions of the new room, in inches, on the blueprint? What will the dimensions of the new room be, in feet, in the new house?
the new coordinates of the room are Q(2.3125, 4.125), R(7.3125, 4.125), S(7.3125, 6.125), and T(2.3125, 6.125). the dimensions of the new room on the blueprint are 5.78125 inches by 2 inches and in feet 0.48 feet by 0.17 feet.
To find the new coordinates of the room, we can first calculate the dimensions of the original room and then increase them by 25%. The length of the room is the distance between points R and S, which is:
√(7-2)² + (4-4)² = 5 units
The width of the room is the distance between points Q and T, which is:
√(2-2)² + (6-4)² = 2 units
To increase the dimensions of the room by 25%, we can multiply the length and width by 1.25.
The new length is: 5 × 1.25 = 6.25 units
The new width is: 2 × 1.25 = 2.5 units
To find the new coordinates of the room, we can add half of the increase in each dimension to the original coordinates.
The new coordinates of Q are: (2 + 0.625/2, 4 + 0.25/2) = (2.3125, 4.125)
The new coordinates of R are: (7 + 0.625/2, 4 + 0.25/2) = (7.3125, 4.125)
The new coordinates of S are: (7 + 0.625/2, 6 + 0.25/2) = (7.3125, 6.125)
The new coordinates of T are: (2 + 0.625/2, 6 + 0.25/2) = (2.3125, 6.125)
Therefore, the new coordinates of the room are Q(2.3125, 4.125), R(7.3125, 4.125), S(7.3125, 6.125), and T(2.3125, 6.125).
To find the dimensions of the new room in inches on the blueprint, we can use the Pythagorean theorem: The new length is:
√(7.3125-2.3125)² + (4.125-4.125)² = 5.78125 units
The new width is: √(7.3125-7.3125)² + (6.125-4.125)² = 2 units
Therefore, the dimensions of the new room on the blueprint are 5.78125 inches by 2 inches.
To find the dimensions of the new room in feet in the new house, we can convert the dimensions to feet by dividing by 12:
The new length is: 5.78125 inches / 12 inches/ft = 0.48 ft
The new width is: 2 inches / 12 inches/ft = 0.17 ft
Therefore, the dimensions of the new room in the new house are 0.48 feet by 0.17 feet.
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Complete Question
A rectangular room has coordinates Q (2, 4), R(7, 4), 5 (7, 6), and T(2, 6) on the blueprint. The homeowner wants the dimensions of this room to be 25% larger. What are the coordinates of the new room? What are the dimensions of the new room, in inches, on the blueprint? What will the dimensions of the new room be, in feet, in the new house?
A researcher suspects that the mean birth weights of babies whose mothers did not see a doctor before delivery is less than 3000 grams. The researcher states the hypotheses as
The researcher's hypotheses for this study are:
H0: The mean birth weight of babies whose mothers did not see a doctor before delivery is equal to or greater than 3000 grams.
Ha: The mean birth weight of babies whose mothers did not see a doctor before delivery is less than 3000 grams.
In this case, the null hypothesis (H0) states that there is no difference in the mean birth weight of babies whose mothers did not see a doctor before delivery and the mean birth weight of 3000 grams. The alternative hypothesis (Ha) states that the mean birth weight of babies whose mothers did not see a doctor before delivery is less than 3000 grams.
To test these hypotheses, the researcher will need to collect data on the birth weights of babies whose mothers did not see a doctor before delivery and compare the mean birth weight to 3000 grams. If the mean birth weight is significantly less than 3000 grams, the researcher will reject the null hypothesis and accept the alternative hypothesis. If the mean birth weight is not significantly less than 3000 grams, the researcher will fail to reject the null hypothesis.
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Which expressions are equivalent to
35
+
30
�
−
45
�
35+30s−45t35, plus, 30, s, minus, 45, t?
The expressions which are equivalent to 35 + 30s - 45t are:
5(7+6s−9t)
(−35−30s+45t)×(−1)
The correct answer options are options B and C
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
We have to determine equivalent expression:
35 + 30s - 45t
Check all options
A. 7⋅(5+30s−45t)
= 35 + 210s - 315t
False
B. 5(7+6s−9t)
= 35 + 30s - 45t
True
C. (−35−30s+45t)×(−1)
= 35 + 30s - 45t
True
D. 10×(3.5+3s−4.5)
= 35 + 30s - 45
False
E. ( 35/2 - 15s + 45/2t) ⋅ (-2)
= (17.5 - 15s + 22.5t) (-2)
= -35 + 30s - 45t
False
Therefore, the equivalent expression is an expression which has an equal value to each other.
Complete question:
Which expressions are equivalent to 35 + 30s - 45t?
A. 7⋅(5+30s−45t)
B. 5(7+6s−9t)
C. (−35−30s+45t)×(−1)
D. 10×(3.5+3s−4.5)
E. ( 35/2 - 15s + 45/2t) ⋅ (-2)
choose 2 answers
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16. A farmer wants to build a rectangular pasture that has an area represented by 20x6y5. He has
enough room for the length to be 5x³y4. How wide would he need to make the pasture?
The width he need to make the pasture with the given rectangle is 4x³y⁶.
How does area of a rectangle, and its length and width are related?
Area of a rectangle is the product of its length and width.
If a rectangle has length L units and width of W units, then
Area = L × W squared units.
We are given that;
Area= 20x6y5
Length= 5x³y4
We can start by using the formula for the area of a rectangle:
Area = length x width
We know that the area of the rectangular pasture is 20x6y5, and we know the length is 5x³y4. So we can plug in these values and solve for the width:
20x6y5 = (5x³y4) x width
To solve for width, we can divide both sides by 5x³y4:
width = 20x6y5 / (5x³y4)
Simplifying the expression on the right-hand side, we can divide each term in the numerator by 5x³y4:
width = (4x³y¹) x (4y5)
Simplifying further, we can add the exponents of the common factor y:
width = 4x³y⁶
Therefore, the farmer would need to make the width of the rectangular pasture will be 4x³y⁶.
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how to convert 200 mph in km?
200 mph is approximately equal to 321.86 km per hour ( rounded to two decimal places )
The conversion factor to convert mph to km per hour is 1.6093
1 mph = 1.6093 km per hour
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
The speed in km per hour = The speed in mph × conversion factor
Substitute the values in the equation
1 mph = 1.6093 km per hour
200 mph = 1.6093 × 200
Multiply the numbers
= 321.86 km per hour ( rounded to two decimal places )
Therefore, 200 mph is 321.86 km
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What are the 5 steps to solving an inequality?
The five steps to solving an inequality are as follows:
1.Identify the inequality - In the equation, the inequality symbol should be identified first.
2.Isolate the variable - The inequality should be rearranged so that the variable is on one side, and all other terms are on the other side.
3.Simplify the inequality - Multiplication and division rules should be used to simplify the equation.
4.Solve the inequality - The simplified inequality can be solved for the variable.
5.Graph the solution - The solution should be graphed on a number line in order to visualize it.
In summary, solving an inequality requires the identification of the inequality symbol, the isolation of the variable, the simplification of the inequality, the solving of the inequality, and the graphing of the solution. Following these steps carefully will ensure that the inequality is solved accurately.
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Its asking to solve and substitue, what do i substitue and solve?
The solutions of the given equation are 3.16, 1, and - 1.
Solutions of equations:All numbers that make an equation true when the unknowns are eliminated from the equation are considered the solution of the equation.
For the given equation, we can find the solutions by factorizing as shown below.
Here finding the factors of the given polynomial is known as Factorizing. In other words, writing the given equation as a product of its factors.
Here we have
x⁴ - 11x² + 10 = 0
We can solve the above equation as follows
x⁴ - 11x² + 10 = 0
x⁴ - 10x² - x² + 10 = 0
Group out the like terms
x²(x² - 10) - (x² - 10) = 0
(x² - 10) (x² - 1) = 0
(x² - 10) (x - 1)(x + 1) = 0 [ ∵ (x² - 1²) = (x - 1)(x + 1) ]
x² - 10 = 0 => x = √10 = 3.16
x - 1 = 0 => x = 1
x + 1 = 0 => x = -1
Therefore,
The solutions of the given equation are 3.16, 1, and - 1.
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pls help I need this my the end of today
If function [tex]f(x) = 7x - 8[/tex] and [tex]g(x) =4[/tex] then the answer is [tex](fog)(-1) = -36.[/tex]
Describe Function?In mathematics, a function is a relation between two sets of values, where each input value from the first set (called the domain) corresponds to exactly one output value in the second set (called the range). The output value of a function is determined by its input value and any relevant rules or formulas.
Formally, a function can be defined as follows: Let X and Y be two non-empty sets. A function f from X to Y is a rule or formula that assigns to each element x in X a unique element y in Y, denoted by f(x), such that for any two elements x1 and x2 in X, if x1 = x2, then f(x1) = f(x2). The set X is called the domain of the function, and the set Y is called the codomain or range of the function.
Functions can be represented graphically, algebraically, or in tabular form. The graph of a function shows how the output value of the function varies with the input value, and can be used to visualize the behaviour of the function. The algebraic representation of a function can be given by a formula or equation that expresses the output value in terms of the input value. A tabular representation of a function shows the input-output pairs in a table.
Functions are used in many areas of mathematics, science, engineering, and economics to model and describe relationships between variables. They are also used in practical applications, such as in computer programming, where they are used to define algorithms and data structures.
We need to find (fog)(-1) = f(g(-1)).
First, we find g(-1):
g(-1) = 4(-1) = -4
Then, we plug in g(-1) into f:
f(g(-1)) = f(-4) = 7(-4) - 8 = -36
Therefore, (fog)(-1) = -36.
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