Answer:
19 - 42x
Step-by-step explanation:
To differentiate this, we must use the product rule
f'(x) = (7x+3)'(4-3x) + (4-3x)'(7x+3)
= (7)(4-3x) + (-3)(7x+3)
= 28 - 21x - 21x - 9
= 19 - 42x
To stay healthy, Emily decided to walk for mile every day. She walked mile to work and walked mile at lunchtime. How much more does she need to walk after dinner if she wants to meet her target distance?
Based on fractional subtraction, Emily must walk ¹/₂₀ miles after dinner to meet her target walking distance of ⁴/₅ miles daily.
What is a fraction?A fraction represents a portion or part of a whole value.
Subtractions involving fractions can be accomplished by finding the common factor of the denominators as follows:
The target walking distance that Emily set = ⁴/₅ miles
The distance Emily covered to work = ²/₅ miles
The distance Emily covered during lunchtime = ¹/₄ miles
The distance that Emily needs to walk after dinner to meet her set target = ¹/₂₀ (⁴/₅ - ²/₅ - ¹/₄)
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Complete Question:To stay healthy, Emily decided to walk 4/5 miles every day. She walked 2/5 miles to work and walked 1/4 mile at lunchtime. How much more does she need to walk after dinner if she wants to meet her target distance?
Evaluate the expression below.
16)
Chapter
2^5• (−2) – 4 •5+7
The numeric value of the expression in this problem is given as follows:
-77.
How to obtain the numeric value of the expression?The expression in the context of this problem is defined as follows:
[tex]2^5[/tex] x (-2) - 4 x 5 + 7.
Considering the PEMDAS acronym, the power operation has the precedence over the remaining operations, hence:
[tex]2^5[/tex] x (-2) - 4 x 5 + 7 = 32 x (-2) - 4 x 5 + 7.
Then, following the same acronym, we have that the multiplication operation has precedence over the addition/subtraction operations, hence:
32 x (-2) - 4 x 5 + 7 = -64 - 20 + 7.
Finally, we can just subtract and add the numbers to obtain the numeric value of the expression as follows:
-64 - 20 + 7 = -77.
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Work out the area of this circle.
Give your answer in terms of and state its units.
TC
14 cm
Answer:
49pi cm^2
Step-by-step explanation:
The area of a circle is pi(r)^2
To find our radius, we need to divide the diameter by 2.
14 / 2 = 7
Lets plug that into our equation:
pi(7)^2
Simplify:
pi(49)
rearrange:
49pi
WAIT, we need units!
49pi cm^2
~~~Harsha~~~
1.2 If Erin had 150m/ of buttermilk and recipe require 0.25 cups of buttermilk, would Erin have enough buttermilk for the recipe (2) 1.3 A cake recipe calls for 0.8 kg of flower, 650g of sugar and 900 000mg of butter. 1.3.1 Determine the total mass of the ingredients. Give you answer in kilograms. (2) 1.3.2 If sugar comes in 150g bags at cost of R5.95 per 150g, determine the total cost of the (2) sugar needed for this recipe.
If Erin had 150m/ of buttermilk and recipe require 0.25 cups of buttermilk, she has more than the required amount, so she has sufficient buttermilk for the recipe.
1.2 To determine if Erin has enough buttermilk for the recipe, we need to convert the given quantities to a common unit.
150 ml of buttermilk is equivalent to 0.15 liters (since 1 liter = 1000 ml).
Now, let's convert 0.25 cups to liters. Since 1 cup is approximately 0.2366 liters, we have:
0.25 cups ≈ 0.25 * 0.2366 liters = 0.05915 liters.
Comparing the amount of buttermilk Erin has (0.15 liters) with the amount required by the recipe (0.05915 liters), we can see that Erin has enough buttermilk. She has more than the required amount, so she has sufficient buttermilk for the recipe.
1.3.1 To determine the total mass of the ingredients, we need to convert the given quantities to a common unit, kilograms.
0.8 kg of flour is already in kilograms.
650 g of sugar is equivalent to 0.65 kg (since 1 kg = 1000 g).
900,000 mg of butter is equivalent to 900 g (since 1 g = 1000 mg), which is 0.9 kg.
Adding up the masses of the ingredients:
0.8 kg (flour) + 0.65 kg (sugar) + 0.9 kg (butter) = 2.35 kg.
Therefore, the total mass of the ingredients is 2.35 kilograms.
1.3.2 If sugar comes in 150 g bags at a cost of R5.95 per 150 g, we can calculate the total cost of the sugar needed for the recipe.
The recipe requires 650 g of sugar. Since each bag contains 150 g of sugar, we divide the required amount by 150 g:
650 g / 150 g = 4.3333 bags.
Since we cannot purchase a fraction of a bag, we need to round up to the nearest whole number. So, we'll need to buy 5 bags of sugar.
The total cost of the sugar is calculated by multiplying the number of bags by the cost per bag:
5 bags * 5.95 per bag = 29.75.
Therefore, the total cost of the sugar needed for the recipe is 29.75.
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Jaxon is flying a kite, holding his hands a distance of 3.25 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 24
∘
∘
. If the string from the kite to his hand is 105 feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.
divide 16x³+31.6x²-6.8x-12 by x+2
Answer:
16x^2 - 1.6x - 5
------------------------
x+2 | 16x^3 + 31.6x^2 - 6.8x - 12
- (16x^3 + 32x^2)
------------------------
-0.4x^2 - 6.8x
+(-0.4x^2 - 0.8x)
-----------------
-6x - 12
+(-6x - 12)
----------
0
Answer: = 16x²-.4x-6
Step-by-step explanation:
divide 16x³+31.6x²-6.8x-12 by x+2
Using synthetic division: Carry first 1 down. Multiply that by outside -2 and put it under 2nd number. Add. Then multiply and repeat until you get to end.
-2 | 16 31.6 -6.8 -12
| -32 .8 12
16 -.4 -6 0
Put back into equation form. Last number is 0 so remainder is 0
= 16x²-.4x-6
Evaluate 6x + 5y for x = 5 and y = 3.
Answer:
45
Step-by-step explanation:
Plug in the numbers with their variables.
6(5)+5(3)
30+15
45
Hope this helps
what is the value of (-3/4)^-4
Answer:
To calculate the value of (-3/4)^-4, we need to apply the exponentiation rules.
When a negative number is raised to an even power, the result is positive. Thus, we can rewrite (-3/4)^-4 as (4/-3)^4.
Now, let's evaluate the expression:
(4/-3)^4 = (4^4)/(-3)^4 = 256/81
So, the value of (-3/4)^-4 is 256/81
Step-by-step explanation:
⌢
In circle D, m∠EDF=70∘, and the length of EF=[tex]\frac{14}{9} \pi[/tex]. Find the length of DE.
To find the length of DE in circle D, we can use the properties of a circle and the given information.
In a circle, if two chords intersect, the product of the segments of one chord is equal to the product of the segments of the other chord. In this case, we have chord EF intersecting chord DE at point D.
Let x represent the length of segment DE, and y represent the length of segment DF. Therefore, the length of segment EF would be (x + y).
According to the chord-chord power theorem:
DE * EF = DF * DF
Substituting the given values:
x * (x + y) = y * y
x^2 + xy = y^2
We are also given that angle EDF measures 70 degrees. According to the angle intercepting chord theorem, the intercepted arc EF is twice the measure of angle EDF. So, the measure of arc EF is 2 * 70 = 140 degrees.
Now, we can use the length of arc EF to find the ratio of the lengths of segments EF and DF.
The ratio of the lengths of the intercepted arcs is equal to the ratio of the lengths of the corresponding chords. Therefore:
EF / DF = arc EF / arc DF
(x + y) / y = 140 / 360 [Using the measure of the intercepted arcs]
Simplifying this equation:
(x + y) / y = 7 / 18
Cross-multiplying:
18(x + y) = 7y
18x + 18y = 7y
18x = 7y - 18y
18x = -11y
Dividing by -11:
x = -11y / 18
We need to find the value of x, which represents the length of segment DE. Since segment lengths cannot be negative, we can disregard the negative sign.
x = 11y / 18
Substituting this value of x in the equation x^2 + xy = y^2:
(11y / 18)^2 + (11y / 18) * y = y^2
Simplifying:
121y^2 / 324 + 11y^2 / 18 = y^2
Multiplying through by 324:
121y^2 + 594y^2 = 324y^2
715y^2 = 324y^2
715y^2 - 324y^2 = 0
391y^2 = 0
y^2 = 0
Since y^2 = 0, it implies that y = 0. This means that segment DF has zero length.
Now, substituting y = 0 into the equation x = 11y / 18:
x = 11 * 0 / 18
x = 0
Therefore, the length of DE is 0.
In conclusion, the length of DE is 0.
I cannot load the image that you have provided this is what the answer is according to the text provided.
Question 6 Which of the following is the graph of f(x) = x² = 5x + 4?
Given: The equation x² = 5x + 4
We have to draw the the graph for the given equation.
Consider the given equation,
x^2 - 5x - 4 = 0
The vertex of the parabola of the form f(x) = ax^2 + bx + c is given by x = -b/2a
Here,
a= 1
b= -5
c= -4
vertex = x = 5/2= 2.5
Also, the y coordinate at x = 2.5 is,
y = (2.5)^2 -5(2.5)-4
y = -10.25
Thus the vertex of parabola is (2.5 , -10.25)
y - intercept is the point where x = 0
put x = 0 in given equation
f(x) = 0 - 0 -4
f(x) = -4
hence y intercept is at (0, -4).
Now, we calculate x- intercept
x- intercept is where y is equal to 0.
Put f(x) = 0
We have,
x^2 - 5x - 4 = 0
by using quadratic formula,
x = -b ±√b² - 4ac/2a
x=5 ±√-5² - 4 (1)(-4)/2
x= 5±√41/2.
Hence with the obtained values the graph of the equation is obtained.
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HI HELLO ITS MATH I. NEED HELP
Formula for slant height:
[tex]l = \sqrt{ {r}^{2} + {h}^{2} } [/tex]
We dont have height so we will find it with the help of area
[tex] \sf \: area = \pi {r}^{2} + \sqrt{ {r}^{2} + {h}^{2} } [/tex]
[tex] \sf \: 31.4 = 3.14 \times {2}^{2} + \sqrt{ {2}^{2} + {h}^{2} } [/tex]
[tex] \sf \: 31.4 = 3.14 \times 4 + \sqrt{ 4 + {h}^{2} } [/tex]
[tex] \sf \: 31.4 =12.56 + \sqrt{ 4 + {h}^{2} } [/tex]
[tex] \sf \: 31.4 - 12 .56 = \sqrt{ 4 + {h}^{2} } [/tex]
[tex] \sf \: 18.84 = \sqrt{ 4 + {h}^{2} } [/tex]
[tex] \sf \: 18.84 ^{2} = 4 + {h}^{2} [/tex]
[tex] \sf \: 354.9456 - 4 = {h}^{2} [/tex]
[tex] \sf \: 350.9456 = {h}^{2} [/tex]
[tex] \sf \: h = \sqrt{ 350.9456}[/tex]
[tex] \sf \: h = 18.73[/tex]
Now put this in the first formula to find slant height (l)
[tex] \tt \: l = \sqrt{ {r}^{2} + {h}^{2} } [/tex]
[tex] \tt \: l = \sqrt{ {2}^{2} + {18.73}^{2} } [/tex]
[tex] \tt \: l = \sqrt{ 4 + 350.8129 } [/tex]
[tex] \tt \: l = \sqrt{ 354.8129 } [/tex]
[tex] \tt \: l = 18.83[/tex]
PLS HELP MEEEE PLSSS The number of defective watches manufactured by a watch company, with regard to the total number of watches manufactured for each
order, are shown in the scatter plot below.
Which of the equations below would be the line of best fit?
A. y = 1/5x
B. y = 1/50x
C. y = 1/50x-10
D. y = 1/50x+10
The equation that would be the line of best fit is B. y = 1/50x
How to calculate the valueThe line of best fit is a line that best describes the relationship between two variables. In this case, the two variables are the total number of watches manufactured and the number of defective watches. The line of best fit is determined by finding the line that minimizes the sum of the squared vertical distances between the line and the data points.
The line of best fit for the scatter plot is y= 1/50x. This line passes through the center of the data points, which means that it minimizes the sum of the squared vertical distances between the line and the data points. The slope means that for every 50 watches manufactured, there is one defective watch.
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Tom buys a UNC jersey with a 20% discount coupon.
Which response accurately calculates his new cost C
with respect to the original costs x?
a. C=x-0.20
B. C = 0.80x
C. C = 1.20x
d. C = x-0.80
Match the prompts together.
When matched, the prompts on asymptotes would be:
Vertical asymptote at x=0: The cost of producing pills can never reach 0.Decreasing on (0,∞): As the number of pills produced gets smaller, the average cost of production greatly increases.Horizontal asymptote at y=0: The cost of producing pills cannot be negative.Positive on (0,∞): As more pills are produced, the average cost per pill decreases.How to match the asymptote statements ?The presence of a vertical asymptote at x=0 signifies that the cost of producing pills can never reach a value of 0, remaining persistently positive. Simultaneously, the horizontal asymptote at y=0 serves as a reassuring indication that the cost of producing pills cannot be negative, as it steadfastly remains at or above zero.
This crucial constraint ensures that the cost incurred in the pill production process is always a non-negative quantity. Consequently, the prompt related to the impossibility of negative costs aligns with this notion.
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determine the value of
�
(
�
∩
�
)
P(A∩B), rounding to the nearest thousandth, if necessary.
The probability of the intersection P(A∩B) is 0
What is the probability of the intersection P(A∩B)From the question, we have the following parameters that can be used in our computation:
Event A = 18
Event B = 12
Intersection = 0
Other Events = 6
Using the above as a guide, we have the following:
Total = A + B + C
So, we have
Total = 18 + 12 + 6
Evaluate
Total = 36
So, we have
P(A) = 18/36
P(B) = 12/36
For the intersection events, we have
P(A∩B) = 0/36
Evaluate
P(A∩B) = 0
Hence, the probability of P(A∩B) is 0
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Megan has two books that each have dimensions of 12 inches x 6 inches x 2 inches. What is the volume, in cubic inches, of Megan's two books?
Answer:
288in³
Step-by-step explanation:
volume for one = 12 X 6 X 2 = 144.
for two books, it is 2 X 144 = 288in³
A student is given the triangle attached. The student claims that sin(20°)=x/5in. Explain why this reasoning is incorrect.
The reasoning of the student is wrong because the claim doesn't abide by the sine rule and formula.
What is a sine rule and formula?The sine rule states that in a triangle, side “a” divided by the sine of angle A is equal to the side “b” divided by the sine of angle B is equal to the side “c” divided by the sine of angle C.
That is;
a/sinA= b/sinB = c/sinC
Therefore, the proper equation to find X = 5/sin98° = X/sin20°
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Complete the square to rewrite y = -x2 + 8x - 7
Answer:
x = 1 or x = 7
Step-by-step explanation:
-x² + 8x - 7
= -(x² - 8x) - 7
= - [(x - 4)² - 16] - 7
= -(x - 4)² + 16 - 7
= -(x - 4)² + 9.
-(x - 4)² + 9 = 0
-(x - 4)² = -9
(x - 4)² = 9
x - 4 = ±√9
x - 4 = ±3
x = 3 + 4 or x = -3 + 4
x = 7 or x = 1
William Oughtred is most famous not for his mathematical discoveries, but rather for introducing two mathematical symbols. What are they?
The two mathematical symbols that William Oughtred introduced are "×" for multiplication and "::" for proportion.
Given is a statement about William Oughtred.
William Oughtred is most famous not for his mathematical discoveries, but rather for introducing two mathematical symbols.
We have to find those symbols.
William Oughtred is actually an English priest who basically teaches the students in mathematics subject.
He did invent other famous things like slide rule.
But the most famous invention of him is two mathematical symbols which are "×" for multiplication and "::" for proportion which are still widely used symbols.
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How do you determine a the coordinates
The figure below shows part of a circle, with central angle as marked.
What part of the full circle does the figure represent? Express your
answer as a fraction in simplest terms.
290
Prior to June 30, a company has never had any treasury stock transactions. The company repurchased 185 shares of its $1 par common stock on June 30 for $42 per share. On July 20, it reissued 90 of these shares at $46 per share. On August 1, it reissued 70 of the shares at $40 per share. What is the journal entry necessary to record the reissuance of treasury stock on July 20?
On July 20, the journal entry to record the reissuance of treasury stock is: Debit Cash for $4,140 and credit Treasury Stock for $4,140.
To record the reissuance of treasury stock on July 20, the company needs to make the following journal entry:
Date: July 20
Account Debit Credit
Cash $4,140
Treasury Stock $4,140
Explanation:
Debit to Cash ($46 per share * 90 shares) to record the cash received from the reissuance of 90 shares of treasury stock: $46 * 90 = $4,140.
Credit to Treasury Stock to remove the cost of the 90 reissued shares from the treasury stock account.
This journal entry reflects the cash inflow from the reissuance of treasury stock and reduces the balance in the treasury stock account, indicating a reduction in the number of shares held by the company as treasury stock.
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HII PLEASE FILL OUT THE CROSSWORD PUZZEL FOR ME
Answer:
what is all that?!
Which statement correctly compares the centers of the distributions? A. The median of Southview HS is greater than the median of East Hills HS B. The mean of Southview HS is greater than the mean of East Hills HS C.The range of East Hills HS is greater than the range of Southview HS D. The Mean of East Hills HS is greater than the Mean of South view HS
The statement that correctly compares the centers of the distributions is this:
D. The mean of East Hills HS is greater than the mean of Southview HS.
Since, The statement that correctly describes the centers of the distributions is option D. To find out, we will calculate the mean of the two distributions as follows:
For East Hills HS
25 * 1 + 29 * 1 + 31 * 2 + 33 * 4 + 35 * 5 + 37 * 8 + 39 * 4
= 875
And, Frequency = 1 + 1 + 2 + 4 + 5 + 8 + 4 = 25
Hence,
Mean = 875/25
Mean = 35
For Southview
25 * 2 + 27 * 6 + 29 * 9 + 31 * 6 + 33 * 2
= 725
Frequency = 2 + 6 + 9 + 6 + 2 =25
Hence, Mean = 29
So, from our calculation, the mean of East Hills HS is greater than the mean of Southview HS.
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Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:
x = 36.1°
Step-by-step explanation:
In the Right-angled triangle, opposite side of angle x and adjacent side of angle x is given, and we have to find the angle x. To find angle x, we can use the trigonometry ratio 'tan x'.
[tex]\sf Tan \ x = \dfrac{opposite \ side \ of \ \angle X}{adjacent \ side \ of \ \angle x}[/tex]
[tex]\sf = \dfrac{22}{30}\\\\ = 0.73[/tex]
[tex]x = arctan \ (0.73)[/tex]
= 36.13
x = 36.1°
The ideal diameter for a cake is 24 in. A chef wants to purchase a cake with
a margin of error of 3 inches. Describe this statement using an absolute
value equation.
By using this absolute value equation, the chef can determine the range of cake diameters that meet the desired margin of error of 3 inches and make an informed decision when purchasing the cake.
The absolute value of the difference between the actual diameter of the cake and the ideal diameter of 24 inches should be less than or equal to 3 inches.
To describe the statement using an absolute value equation, let's define the variable "d" as the actual diameter of the cake.
The ideal diameter of the cake is given as 24 inches.
The margin of error is specified as 3 inches, which means the chef is willing to accept a cake with a diameter within 3 inches of the ideal size.
Considering the margin of error, we can express the acceptable range of diameters for the cake as follows:
d - 24 ≤
This inequality states that the difference between the actual diameter "d" and the ideal diameter of 24 inches should be less than or equal to 3 inches, indicating that the actual diameter should be no more than 3 inches larger or smaller than 24 inches.
However, to represent this condition using an absolute value equation, we need to remove the inequality signs.
We can rewrite the inequality above using absolute value:
|d - 24| ≤ 3
This absolute value equation states that the absolute value of the difference between the actual diameter "d" and the ideal diameter of 24 inches should be less than or equal to 3 inches.
It encompasses both possibilities of the actual diameter being within 3 inches greater or smaller than 24 inches.
By using this absolute value equation, the chef can determine the range of cake diameters that meet the desired margin of error of 3 inches and make an informed decision when purchasing the cake.
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i need help with the attached questions. thank you
Yes, because it is practical to obtain that many aspirin because the number is relatively small. The correct option is B.
The minimum sample size required to be 99% confident that the sample standard deviation (s) is within 10% of the population standard deviation (σ) is 336, according to the table provided.
This means that in order to have a high level of confidence (99%) that the sample standard deviation is within a reasonable range of the population standard deviation, a minimum sample size of 336 is needed.
In this case, the sample size requirement is met with a relatively small number, 336, compared to the larger values provided in the table for higher levels of confidence.
Therefore, it can be considered practical to obtain that many aspirin tablets for the purposes of this study.
Thus, the correct option is B.
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What numbers could go in the blanks so that this represents y as a function of x? {(2,7), (5,14), (x,y), (9,21)}
Every pair of values except (2, y different of 7), (5, y different of 14) and (9, y different of 21) can go in the blanks so that this represents y as a function of x.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.
For a point in the standard format (x,y), we have that:
x is the input.y is the output.The meaning is that the input given by the x-coordinate is mapped to the output given by the y-coordinate.Hence every point can go into the blank, except the ones that map the inputs 2, 5 and 9 to different outputs than the ones already given in this problem.
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What the meaning of statement this?
Yes, the product of X and Y, that is X × Y is a set.
Given that, the product X×Y is a set because X×Y⊂PP(X∪Y).
A set is defined as a collection of elements or members, and X × Y meets this criteria as it is a collection of ordered pairs of elements from X and Y.
We can also prove this using set theory. The expression X × Y⊂PP(X∪Y) means that the set X × Y is a subset of the power set of the union of X and Y.
The power set of a set A is a set of all subsets of A, which means that PP(X∪Y) includes all of the possible combinations of the elements from X and Y.
So, the fact that X × Y⊂PP(X∪Y) proves that it is a subset of a set and thus is a set itself.
Yes, the product of X and Y, that is X × Y is a set.
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Amelia runs a day care center. So far this year, the enrollment has consisted of 3 babies and 6 children of other ages. Considering this data, how many of the next 12 children to enroll should you expect to be babies? PLS HURRY
Answer:
Hope this saved you ^^
Step-by-step explanation:
To determine the number of babies we can expect among the next 12 children to enroll, we need to calculate the proportion of babies based on the current enrollment data.
Out of the total enrollment so far, there are 3 babies and 6 children of other ages, making a total of 9 children.
Proportion of babies = (Number of babies / Total number of children) = 3 / 9 = 1/3
Now, to estimate the number of babies among the next 12 children, we multiply the proportion of babies by the total number of children to be enrolled:
Number of babies expected = Proportion of babies * Total number of children to enroll
Number of babies expected = (1/3) * 12 = 4
Therefore, based on the current enrollment data, we can expect approximately 4 out of the next 12 children to be babies.