Please help if you can calculate it!
A survey was conducted one month ago to review the calories of lunch boxes provided by the supplier "Better
Lunch". In a sample with 300 lunch boxes, there were 273 lunch boxes with calories below 650 and the other
27 lunch boxes with calories above 650. Besides, the mean calories was 550 and standard deviation was 40.
(a) Find the point estimate of the population proportion of lunch boxes provided by "Better Lunch" had
calories above 650.
(b) Calculate the sampling error at 98% confidence level for the estimate of the population proportion of
lunch boxes provided by "Better Lunch" had calories above 650.
(c) Construct a 98% confidence interval estimate of the population proportion of lunch boxes provided by
"Better Lunch" had calories above 650.
(d) "Better Lunch" follows government's suggestions to change the menu in order to reduce the lunch boxes'
calories. Suppose after the menu update, each lunch box's calories can be reduced by 4%. Find the
sample mean and sample standard deviation of calories of the above sample after the change. Hence,
construct a 90% confidence interval estimate of the population mean calories in a lunch box after the
change.
Answers
The 90% confidence interval estimate of the population mean calories in a lunch box after the change is between 524.2 and 531.8.
How to construct a 90% confidence interval estimate of the population mean calories in a lunch box after the change.(a) The point estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is 0.09, which is equal to 27/300.
(b) The sampling error at 98% confidence level for the estimate of the population proportion can be calculated using the following formula:
Sampling error = z*(standard deviation/square root of sample size)
Where z is the critical value at 98% confidence level, which can be found using a standard normal distribution table or calculator. For a 98% confidence level, the z value is 2.33.
Substituting the values, we get:
Sampling error = 2.33*(sqrt(0.09*0.91/300)) = 0.049 or 4.9%
Therefore, the sampling error at 98% confidence level for the estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is 4.9%.
(c) The 98% confidence interval estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 can be calculated using the following formula:
Confidence interval = point estimate ± (z*standard error)
Where point estimate is 0.09, z is the critical value at 98% confidence level which is 2.33, and standard error is the standard deviation divided by the square root of sample size.
Substituting the values, we get:
Confidence interval = 0.09 ± (2.33*sqrt(0.09*0.91/300)) = 0.09 ± 0.114 or (0.026, 0.154)
Therefore, the 98% confidence interval estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is between 0.026 and 0.154.
(d) After the menu update, the sample mean of the calories of the above sample can be calculated as follows:
New sample mean = 0.96 * 550 = 528
The sample standard deviation after the change is still 40, assuming the variability of calories is not affected by the menu update.
To construct a 90% confidence interval estimate of the population mean calories in a lunch box after the change, we can use the following formula:
Confidence interval = sample mean ± (t*standard error)
Where t is the critical value at 90% confidence level with degrees of freedom (df) = sample size - 1. Using a t-distribution table or calculator with df = 299, we find that t = 1.645.
The standard error can be calculated as follows:
Standard error = standard deviation/sqrt(sample size) = 40/sqrt(300) = 2.31
Substituting the values, we get:
Confidence interval = 528 ± (1.645*2.31) = 528 ± 3.8 or (524.2, 531.8)
Therefore, the 90% confidence interval estimate of the population mean calories in a lunch box after the change is between 524.2 and 531.8.
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Related Questions
Can you write equation in conic form?
Answers
The equation x = 1/16y² - 1/8y + 17/16 in conic form is (y - 1)² = 16(x - 1)
Writing the equation in conic form?From the question, we have the following parameters that can be used in our computation:
x = 1/16y² - 1/8y + 17/16
Multply through the equation by 16
S, we have
16x = y² - 2y + 17
Rewrite as
16x - 17 = y² - 2y
Add the square of half the coefficient of y to both sides
So, we have
16x - 17 + 1 = y² - 2y + 1
Evaluate and express as perfect squares
16x - 16 = (y - 1)²
Factor out 16
16(x - 1) = (y - 1)²
Rewrite as
(y - 1)² = 16(x - 1)
The above equation is an equation of a parabola whose inverse has been calculated
Hence, the conic equation is (y - 1)² = 16(x - 1)
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Kevin answered 62 questions correctly on his multiple choice history final and earned a grade of 31%. How many total questions were on the final exam?
Answers
Answer:
200
Step-by-step explanation:
Turn the 31% back to a decimal = 0.31
62/ x = 0.31
multiply each side of the equation by x to cancel it out from under the fraction
62 = 0.31x
divide each side by 0.31 to have to x alone
200 = x
Check work:
62/200 = 0.31 x 100 = 31%
The Wills Tower (formerly known as the Sears Tower) in Chicago is about 454 feet tall A model of it has a scale of 2 in 45 feet. How tall is the model?
Answers
The model is 64.62 inches tall. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
Any real number may be explained using the four basic operations, also referred to as "arithmetic operations." In mathematics, operations like division, multiplication, addition, and subtraction come first, followed by operations like quotient, product, sum, and difference.
We are given that height of tower is 1454 feet and the scale is given as follows:
2 inches = 45 feet
Now, using the division operation, we get
⇒ Height of the model = 1,454 ÷ 45
⇒ Height of the model = 32.31
Now, using the multiplication operation, we get
⇒ Height of the model = 32.31 * 2
⇒ Height of the model = 64.62 inches
Hence, the model is 64.62 inches tall.
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The correct question has been attached below.
La suma de 3 números es 70 el segundo número es el doble del primero y el tercero es el doble del segundo
Answers
The three numbers are 10, 20, and 40.'
How to solveLet's assign variables to each number:
Let x be the first number.Let y be the second number, which is twice the first number (y = 2x).Let z be the third number, which is twice the second number (z = 2y).According to the problem, the sum of these three numbers is 70:
x + y + z = 70
Now, we can substitute the expressions for y and z in terms of x:
x + 2x + 2(2x) = 70
Combine the terms:
x + 2x + 4x = 70
7x = 70
Now, divide by 7 to find the value of x:
x = 70 / 7
x = 10
Now that we have the value of x, we can find the values of y and z:
y = 2x = 2(10) = 20
z = 2y = 2(20) = 40
So, the three numbers are 10, 20, and 40.
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The question in English is
The sum of 3 numbers is 70, the second number is twice the first and the third is twice the second.
calling EXPERTS! Please help with these 3 questions! Please show full solutions AND ALL CALCULATIONS!!! THANK YOU! QUESTIONS ATTACHED BELOW!
Answers
Answer:
2. 139π/90 radians ≈ 4.852
3. -(9√5 +8√7)/77
4. 2+√3
Step-by-step explanation:
You want exact answers involving various trig identities and angle sum formulas.
2. RadiansThere are π radians in 180°, the number of radians in 278° is ...
278°(π/180°) = (278/180)π
278° = (139/90)π radians ≈ 4.852 radians
3. CosineThe cosine of the sum of angles is ...
cos(x +y) = cos(x)cos(y) -sin(x)sin(y)
The relationship between sine and cosine is ...
cos(x) = ±√(1 -sin(x)²)
sin(x) = ±√(1 -cos(x)²)
The signs will depend on the quadrant of the angle.
To use the angle sum relation, we need the sine of the angle whose cosine is given, and vice versa.
sin(arccos(-2/7)) = -√(1 -(-2/7)²) = -(√45)/7 = (-3/7)√5 . . . . in QIII
cos(arcsin(-3/11)) = √(1 -(-3/11)²) = (√112)/11 = (4/11)√7 . . . . in QIV
The cosine of the sum of the angles is then ...
cos(arccos(-2/7) +arcsin(-3/11)) = (-2/7)(4√7/11) -(-3√5)/7·(-3/11)
= -8√7/77 -9√5/77
cos(x +y) = -(9√5 +8√7)/77
4. TangentThe formula for the tangent of the sum of angles is ...
tan(x +y) = (tan(x) +tan(y))/(1 -tan(x)tan(y))
We know that tan(π/4) = 1 and tan(π/6) = 1/√3, so the tangent of the sum of the angles is ...
tan(π/4 +π/6) = (1 +1/√3)/(1 -(1·1/√3)) = (√3 +1)/(√3 -1) = (√3 +1)²/2
tan(π/4 +π/6) = 2 +√3
__
Additional comment
A suitable calculator can be very handy computing and/or checking your results.
2) 278° to Radians = 4.85202
3) the exact value of cos (x+ y) is -0.0914
4) the exact value of the expression is 3.73
How is this so ?The formula ofr conversion from degree to radian is
2) 278° × π/180 = 4.852rad
3) in the above given expressions, Sin(x) is negative.
Using Pythagorean rule, we can state:
sin(x ) = √(1 - cos^2(x)) =
√(1 - (-2/7)²)
= -3√(3)/7
Also,
given that cos( y) is positive, we c n also use the Pythagorean idetity
cos (y) = √(1 - sin ²(y) )
= √(1 - (-3/1 1)²)
= 8√(2)/11
substituting into cos (x + y)
cos(x+y) = cos( x)cos (y ) - sin (x) sin(y)
= (-2/7)( 8 √(2)/11) - (-3√(3)/7) ( -3/11)
= -1 6 √(2) /77 + 9√( 3)/ 77
= -0.09141506142
The exact value is approximately -0.0914
3)
Using the formula for tangent of sum of angles we say
tan( ( π/4) + (π/6) ) = (tan ( π / 4) + tan (π/6))/(1 - tan ( π/4) tan( π/6))
Sutstituting ....
tan (( π/4) + ( π/6) ) = (1 + √ 3/3)/( 1 - √ 3 /3 )
tan( (π/ 4) + (π /6 )) = (1 + √3/ 3) (1 + √3/3 )]/ [(1 - √3/ 3)(1 + √3/3)]
Simplifying
tan ( (π /4) + ( π/6) ) = ( 2 + √3 )/ ( 2 - √ 3)
This is the exact value of tan((π/4) + (π/6)) or 3.73
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The probability that a certain science teacher trips over the cords in her classroom during any independent period of the day is 0.35. On average, how many periods do students need to wait until this science teacher trips over the cords in her classroom?
0.2275
0.35
2.86
3.5
Not enough information to answer this question
Answers
Answer:2.86.
Step-by-step explanation:
We can use the geometric distribution to solve this problem. The geometric distribution models the number of trials needed to achieve the first success in a sequence of independent trials with a constant probability of success.In this case, the probability of success (the teacher tripping over the cords) is 0.35. Therefore, the expected value or mean of the geometric distribution is 1/0.35 ≈ 2.86.So, on average, students need to wait for 2.86 periods until the teacher trips over the cords in her classroom.Therefore, the answer is 2.86.
At a customer service call center for a large company, the number of calls received per
hour is normally distributed with a mean of 90 calls and a standard deviation of 20
calls. What is the probability that during a given hour of the day there will be between
91 calls and 134 calls, to the nearest thousandth?
Answers
Step-by-step explanation:
The number of non square numbers between 12square and 13square are
- Xavier earns a 15% commission on each
washing machine he sells. Last week he sold
four $450 machines. How much did he earn?
Answers
Based on the question, Xavier earned a commission of $270 on the last week.
What is the commission?Commissions is known to be a form of variable-pay remuneration that is said to be made for services given or products sold.
Note that from the question, Xavier earns a 15% commission on all washing machine he sells, so he sold four $450 machines last week.
So, the he total sale of the four machines is:
4 x $450 = $1,800
Since Xavier's commission is 15% of $1,800, it will be calculated as :
Commission = 15% x $1,800
= 0.15 x $1,800
= $270
Hence, Xavier earned a commission of $270 last week.
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The circumference of a circle is 20 cm. What is the
area, in square centimeters? Express your answer in terms
of TT.
Answers
The circumference of a circle whose area is 20π cm² in terms of pi is 8.94π centimeters.
What is the circumference of the circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The area of a circle is expressed mathematically as;
[tex]\text{A} = \pi \text{r}^2[/tex]
The circumference of a circle is expressed mathematically as;
[tex]\text{C} = 2\pi \text{r}[/tex]
Given that the area of the circle is 20π cm², we determine the radius of the circle.
[tex]\text{A} = \pi \text{r}^2[/tex]
[tex]20\pi \ \text{cm}^2 = \pi \times \text{r}^2[/tex]
[tex]\text{r}^2= \dfrac{ 20\pi \ \text{cm}^2}{\pi }[/tex]
[tex]\text{r}^2 = 20 \ \text{cm}^2[/tex]
[tex]\text{r} = \sqrt{20 \ \text{cm}^2}[/tex]
[tex]\text{r} = 4.47 \ \text{cm}[/tex]
Now, we determine the circumference of the circle.
[tex]\text{C} = 2\pi \text{r}[/tex]
[tex]\text{C} = 2 \times \pi \times 4.47 \ \text{cm}[/tex]
[tex]\text{C} = 8.94 \ \text{cm}\times\pi[/tex]
[tex]\text{C} = 8.94\pi[/tex]
Therefore, the circumference of the circle is 8.94π centimeters.
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you are painting a mural of colored equilateral triangles. The radius of each triangle is 12.7 inches. What is the area of each triangle to the nearest square inch?
Answers
The area of each triangle to the nearest square inch is approximately 95 square inches.
What is triangle?A triangle is a 2-dimensional geometric shape that consists of three straight sides and three angles. It is one of the basic shapes in geometry, and it is widely used in various fields such as mathematics, engineering, architecture, and art.
According to given information:To find the area of an equilateral triangle with a radius of 12.7 inches, we can use the formula:
Area = [tex](\sqrt{(3)/4})[/tex] x [tex](side)^2[/tex]
where side is the length of one of the sides of the equilateral triangle.
We know that the radius of the equilateral triangle is 12.7 inches, which means that the distance from the center of the triangle to one of the corners (i.e., the length of one of the sides) is also 12.7 inches. To find the length of the side, we can use the formula for the height of an equilateral triangle:
and solve for side:
side = Height / ([tex]\sqrt{(3)/2[/tex]) = (2 x Height) / [tex]\sqrt{(3)[/tex]
Plugging in the value of the radius, we have:
side = (2 x 12.7 inches) / [tex]\sqrt{(3)[/tex] ≈ 14.67 inches
Now we can use the formula for the area of an equilateral triangle:
Area = ([tex]\sqrt{(3)/4}[/tex]) x [tex](side)^2[/tex]
Plugging in the value of the side, we have:
Area = ([tex]\sqrt{(3)/4[/tex]) x [tex](14.67 inches)^2[/tex] ≈ 94.71 square inches
Therefore, the area of each triangle to the nearest square inch is approximately 95 square inches.
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The 8th grade math team is having a bake sale as a fundraiser. Alan can make 5 cookies in 2 minutes. Abigail can make 8 cookies in 3 minutes. However, Katie eats 1 cookie every 6 minutes. How many minutes will it take to make 5 dozen cookies.
Answers
Answer: B. 12
Step-by-step explanation:
1) Alan can make 2.5 cookies per min
2) Abi can make 8/3 which is 2.7.
3) overall, 5.2 cookies per minute can be made.
multiple 5.2 x 6 and you get around 31.5?
then subtract =1. you have 30.5, now add onto that number 31.5, which is another 6 minutes. since you're still only subtracting 1, the answer would be above 60, which is 5 dozen, and it only took 12 mins
Find the area
Round to nearest tenth
Answers
Split the shape into a rectangle and two triangles
Area of rectangle = 7*18.5
=129.5
Area of triangles = 2(1/2(10.4*15.3)
=159.12
Total area = 159.12+129.5
= 288.62 mm^2
Rounded to the nearest tenth is 288.6
Joan has a square flower bed with a side length of 4 meters filled with tulips. There are a total of 354 tulips in the bed.
Find the density of tulips for the area of the bed. Round to the nearest tenth if necessary.
Answers
If Joan has a square flower bed with a side length of 4 meters filled with tulips, the density of tulips in the bed is 22.1 tulips per square meter.
To find the density of tulips for the area of the bed, we need to divide the total number of tulips by the area of the bed. The area of the square flower bed is the side length squared, so in this case, it is 4 meters x 4 meters = 16 square meters.
So, the density of tulips in the bed is 354/16 ≈ 22.1 tulips per square meter. This means that there are approximately 22.1 tulips growing in every square meter of the flower bed.
The density is a measure of the amount of something per unit of space, so in this case, it is the number of tulips per square meter. It is a useful metric for understanding how many of something is present in a given area, which can be important for planning and management purposes.
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A laptop has a listed price of 639.99 before tax. If the sales tax rate is 9.75%, find the total cost of the laptop with sales tax included. Round your answer to the nearest cent, if necessary.
Answers
Answer: $702.39
Step-by-step explanation: To find the total cost of the laptop with sales tax included, we need to add the sales tax to the listed price.
First, we need to calculate the amount of sales tax.
Sales tax = 9.75% of 639.99
Sales tax = 0.0975 x 639.99
Sales tax = 62.40
Now we can find the total cost of the laptop with sales tax included:
Total cost = listed price + sales tax
Total cost = 639.99 + 62.40
Total cost = 702.39
Therefore, the total cost of the laptop with sales tax included is $702.39.
You paid $6.99 for a shirt that was 70% off; what was the original price of the shirt?
Answers
Answer:
$23.30
Step-by-step explanation:
We Know
You paid $6.99
The shirt was 70% off
$6.99 = 30%
What was the original price of the shirt?
We Take
(6.99 ÷ 30) x 100 = $23.30
So, the original price is $23.30
Use the following chart of years and price for an unstated item to answer the following questions.
1970 1975 1980 1985 1990 1995 2000
$87.32 $119.99 $206.79 $264.16 $283.16 $351.94 $349.69
What was the relative change from 1995 to 2000? (Enter your answer as a percentage rounded to the nearest hundredths.)
Answers
The relative change from 1995 to 2000 is -63.92%, indicating a decrease in price of approximately 63.92%.
How to calculate the relative change?To calculate the relative change from 1995 to 2000, we need to find the difference between the prices in those two years, and then express that difference as a percentage of the price in 1995.
Price in 1995 = $351.94
Price in 2000 = $349.69
Difference = Price in 2000 - Price in 1995
Difference = $349.69 - $351.94
Difference = -$2.25
The negative sign indicates a decrease in price from 1995 to 2000.
Now, we can calculate the relative change as a percentage:
Relative change = (Difference / Price in 1995) * 100
Relative change = (-$2.25 / $351.94) * 100
Relative change = -0.6392 * 100
Relative change = -63.92%
Therefore, the relative change from 1995 to 2000 is -63.92%, indicating a decrease in price of approximately 63.92%.
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y’all which one is it cus ion kno
Answers
equivalent equation for (4x • 7)(5x • 9)
Answers
Another equivalent equation to the equation (4x • 7)(5x • 9) is 28x(45x) respectively.
What are Equivalent equations?Equivalent equations in algebra are those that have equivalent roots or solutions.
In order to produce an equivalent equation, the same quantity or expression must be added to or subtracted from both sides of the original equation.
If you multiply or divide an equation's two sides by the same non-zero number, the results are identical.
If x4=2x+7, we can add 4 to both sides to get the following equation, which is equivalent: x4+4=2x+7+4.
So, we have the equation:
(4x • 7)(5x • 9)
Then, another equation that will be equivalent to the given equation can be:
(4x • 7)(5x • 9)
(28x)(45x )
Then,
28x(45x)
So,
(4x • 7)(5x • 9) = 28x(45x)
Therefore, another equivalent equation to the equation (4x • 7)(5x • 9) is 28x(45x) respectively.
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Find the values of a and b such that
x²-x+ 5 = (x-a)² + b
Please, the person that explains it explain it with the part of
(x+b/2)^2 - (b/2)^2 + c
-because if not I won’t understand :)
Answers
x2−1x5=(x−a)2+b2−15=(−)2+
Solve the following equation for θ on the interval [0,2π).
2sec(θ)+3=0
Round your answers to the nearest thousandth of a radian.
there should be 2 answers
Answers
We can start by isolating the secant term and then taking the inverse cosine of both sides. Remember that the inverse cosine function only gives results on the interval [0,π], so we will need to adjust our solutions accordingly:
2sec(θ) + 3 = 0
2sec(θ) = -3
sec(θ) = -3/2
cos(θ) = -2/3
θ = ±cos⁻¹(-2/3)
Using a calculator, we find:
θ ≈ 2.302, 4.981 radians
What is the value of 0 in the equation?However, we need to adjust these solutions to be within the interval [0,2π). Since cos(x) = cos(2π - x), we can add 2π to the negative solution to get an equivalent positive solution:
θ ≈ 2.302, 7.438 radians
Rounding to the nearest thousandth, we get:
θ ≈ 2.302, 7.438 radians
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Calculate the length of HG. *
10
9
8
6
5
4
3
N
M
H
3
I
5
square root 15
square root 50
square root 8
square root 51
G
9 10
Answers
Using the Pythagorean theorem, we can find the length of HG:
HG² = HI² + IG²
Therefore, the length of HG is 5sqrt(3) units.
What is pythagorean theorem?The Pythagorean Theorem is a mathematical formula that states in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
What is Length?Length is a measurement of the extent of something along its longest dimension, from one end to the other. It is often expressed in units such as meters, feet, or inches.
According to the given information:
To calculate the length of HG, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of its two legs.
First, we can identify that triangle HGN is a right triangle, with HG being the hypotenuse. Using the Pythagorean theorem, we have:
(HG)² = (NG)² + (NH)²
We can also identify that triangle INH is also a right triangle, with IN being the hypotenuse. Using the Pythagorean theorem, we have:
(IN)² = (NH)² + (NI)²
Substituting (NH)^2 from the second equation into the first equation, we get:
(HG)² = (NG)² + (IN)² - (NI)²
Plugging in the values given in the diagram, we get:
(HG)² = 5² + 9² - 3²
(HG)² = 61
HG = √61
Therefore, the length of HG is the square root of 61.
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2 TO THE POWER OF 17 WHAT DA ANSWER
Answers
Answer:
131072
Step-by-step explanation:
Answer: The answer is 131072.
Step-by-step explanation:
Using a calculator, we find that [tex]2^{17}=\boxed{131072}.[/tex]
Which graph represents the question?
Answers
The graph of the piecewise function can be seen in the image attached below where (x+2)² terminates at x = -1, |x - 1| between the interval of x = -1 to x = 1, and [tex]-\sqrt[3]{x}[/tex] from +x-axis to infinity [tex]\infty[/tex]
What is the graph of a piecewise function?A piecewise function is a type of function that has different expressions or formulas for different parts or intervals of its domain. This means that the formula that defines the function changes depending on which part of the domain we are looking at.
Now, to graph the piecewise function, we need to start by identifying the different intervals on which the function is defined and the corresponding expressions that define the function on each interval.
If we have a piecewise function f(x) defined as:
f(x) = (x+2)² for x < -1 is a parabolic function that terminates at x = -1f(x) = |x - 1| for -1 ≤ x ≤ 1, the interval between (-1, 1)f(x) = [tex]-\sqrt[3]{x}[/tex] for x > 1, this includes the values of x for which x > 1 to infinity.The graph of the piecewise function can be seen in the image attached below.
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help my compters dieing
its at 3 percent HELP PLEASE
Answers
Answer: The first number is the X-axis and the second is the Y-axis.
Step-by-step explanation:
5, 1, 4, and 2 belong in X. 35, 7, 28, and 14 belong in Y.
The rule is that X always goes first the Y goes after.
2. y axis.
The bowling average of the players in the Capital Three bowling tournament is 158 with variance of 121. If Dr. Baker bowls an average of 169 during the tournament. Compute the appropriate statistic.
What proportion of bowlers performed better than Dr. Baker?
Answers
Approximately 15.87% of the bowlers in the Capital Three bowling tournament performed better than Dr. Baker.
How to find the proportionStandard deviation (σ) = √(variance) = √(121) = 11
Now, we can calculate the z-score for Dr. Baker's average of 169 using the formula:
z = (X - μ) / σ
z = (169 - 158) / 11
z = 11 / 11
z = 1
Dr. Baker's z-score is 1, meaning his performance is one standard deviation above the mean.
The area to the left (or the cumulative probability) is approximately 0.8413
1 - 0.8413 = 0.1587
Approximately 15.87% of the bowlers in the Capital Three bowling tournament performed better than Dr. Baker.
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What is value of x in this equation:
4x+15=33-2x
Answers
Answer: Simplifying
4x + 15 = 33 + -2x
Reorder the terms:
15 + 4x = 33 + -2x
Solving
15 + 4x = 33 + -2x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '2x' to each side of the equation.
15 + 4x + 2x = 33 + -2x + 2x
Combine like terms: 4x + 2x = 6x
15 + 6x = 33 + -2x + 2x
Combine like terms: -2x + 2x = 0
15 + 6x = 33 + 0
15 + 6x = 33
Add '-15' to each side of the equation.
15 + -15 + 6x = 33 + -15
Combine like terms: 15 + -15 = 0
0 + 6x = 33 + -15
6x = 33 + -15
Combine like terms: 33 + -15 = 18
6x = 18Divide each side by '6'.
x = 3
Simplifying
x = 3
so X=3 is your answer
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Express the statement as an inequality part 7a^2
Answers
The statement, "t is not less than 7" as an inequality is E. t ≥ 7.
The statement, " the negative of z is not greater than 8" is A. - z ≤ 8 .
How to represent as inequalities ?The statement "t is not less than 7" means that t can be equal to 7 or greater than 7, so we can write this as:
t ≥ 7
Therefore, the correct inequality for the statement is t ≥ 7.
Similarly, the statement "the negative of z is not greater than 8" means that the opposite of z, which is -z, can be equal to -8 or less than -8, so we can write this as:
-z ≤ 8
Multiplying both sides of the inequality by -1 gives:
z ≥ -8
Therefore, the correct inequality for the statement is z ≥ -8.
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Answer:
e) The correct option is: t≥7
The phrase "t is not less than 7" means that t can be equal to 7 or any value greater than 7, but it cannot be less than 7. Therefore, we use the greater than or equal to a symbol (≥) to represent this statement.
here's an explanation of each option:
t = 7: This statement indicates that the value of t is exactly 7. If this statement is true, then t cannot be greater than or less than 7.t > 7: This statement indicates that the value of t is greater than 7. If this statement is true, then t can be any value that is greater than 7.t < 7: This statement indicates that the value of t is less than 7. If this statement is true, then t can be any value that is less than 7.t ≤ 7: This statement indicates that the value of t cannot be greater than 7, but it can be less than or equal to 7. If this statement is true, then t can be 7 or any value less than 7.t ≥ 7: This statement indicates that the value of t cannot be less than 7, but it can be greater than or equal to 7. If this statement is true, then t can be 7 or any value greater than 7.To express the statement t≥7 as an inequality in terms of 7a^2, we can simply multiply both sides by 7a^2, like this:t * 7a^2 ≥ 7 * 7a^2
Simplifying the right-hand side of the inequality, we get:49a^2
Therefore, the inequality in terms of 7a^2 is:t * 7a^2 ≥ 49a^2
Note that this inequality is equivalent to t ≥ 7, which is what we started with.
f) The correct option is:-z ≤ 8
The phrase "the negative of z is not greater than 8" means that -z cannot be greater than 8. In other words, -z is less than or equal to 8. To express this as an inequality, we use the less than or equal symbol (≤) and write "-z ≤ 8".
here's an explanation of each option:
Note that only the first option (-z ≤ 8) accurately represents the original statement "The negative of z is not greater than 8". The other options either represent a different statement or contradict the original statement.
The statement "the negative of z is not greater than 8" can be expressed as an inequality in terms of 7a^2 as follows:
-z ≤ 8
Since we cannot multiply or divide by a negative number when we are working with inequalities, we will multiply both sides of the inequality by -1. Remember that whenever we multiply or divide both sides of an inequality by a negative number, we must reverse the direction of the inequality symbol. So, we have:z ≥ -8
Multiplying both sides by 7a^2, we get:7a^2 * z ≥ -8 * 7a^2
Simplifying the right-hand side, we get:-56a^2
Therefore, the inequality in terms of 7a^2 is:7a^2 * z ≥ -56a^2
So, the statement "the negative of z is not greater than 8" can be expressed as the inequality 7a^2 * z ≥ -56a^2.
Mrs. lang has x amount of students in each class. Ms. easter has 4 less students in each class. If both teachers have 5 classes, write an expression that
shows how many students are in all of Ms. easter’s classes.
Answers
If Mrs. Lang has x students in each of her 5 classes, then she has a total of 5x students.
Ms. Easter has 4 less students in each of her classes, so she has x - 4 students in each of her 5 classes.
How many students are in all of Ms. Easter's classes?To find out how many students are in all of Ms. Easter's classes, we can use the expression:
5(x - 4)
This simplifies to:
5x - 20
Therefore, there are 5x - 20 students in all of Ms. Easter's classes.
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5000 people attend a match 50 people win a T-shirt whats the probability of winning a T-shirt
Answers
I need help with this please
Answers
The line plot representing the values on the number line can be presented as follows;
[tex]{}[/tex] ×
[tex]{}[/tex] × ×
[tex]{}[/tex] × × × ×
<-|------|------|------|------|------|------|------|------|->
[tex]{}[/tex]0 1/8 1/4 1/2 5/8 3/4 1
What is line plot?A line plot is a graph displaying data as points above a number, which indicates the frequency of the data.
The values in the fraction can be expressed as follows;
5/8, 5/8, 1/4, 1/8, 1/8, 3/4, 1/8
The values that are repeated can be excluded to get;
Values to be represented are; 5/8, 1/4, 1/8, 3/4
The above fractions can be expressed as fractions with a denominator of 8 as follows;
5/8, 1/4, 1/8, 3/4 = 5/8, 2/8, 1/8, 6/8
The fractions can be arranged in increasing order as follows;
5/8, 2/8, 1/8, 6/8; 1/8, 2/8, 5/8, 6/8
The fractions 1/8, 2/8, 5/8, 6/8, can therefore, be entered into the number line as follows;
<-|------|------|------|------|------|------|------|------|->
0[tex]{}[/tex] 1/8 2/8 1/2 5/8 6/8 1
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