bonus question: math or science :)

Similar shapes have the same angles. These two triangles have no angles in common, so they're not similar.

Size 20% over 3 years

20% 60% 3=60%

Then after 3 years the rat population will be reduced

.

So, after 3 years has changed all that tens of thousands of years

Answer:

1.

a.) 24in

b.)75.36in

c.)452.16in

Step-by-step explanation:

1a. The radius is half of the diameter, so all you have to do is add 12 + 12 which is 24.

1b. the circumfrence of a circle is C (Circumfrence)=\(2\pi r\) so replace radius for 12 and then do 3.14(pi) x 2 which will get you 6.28 times 6.28 by 12 and you will get 75.36.

1c. Area=\(\pi r^{2}\) so first do the radius by the second power, or \(r * r\), susitute r for 12 and you will get 144, times 144 by pi and you will get 452.16in

Sorry I could not answer every question but hope this helps!

(a) There are 81 possible answer sequences for the four questions.

(b) The probability of getting all four answers correct when guessing is approximately 0.01235 when rounded to five decimal places.

(c) The probability of answering at least one question correctly when guessing is approximately 0.51775 when rounded to five decimal places.

(a) Since there are three possible answers for each of the four questions, there are a total of 3^4 = 81 possible answer sequences for the four questions.

(b) If you are guessing on each question, the probability of getting one question correct is 1/3. Since there are four questions, the probability of getting all four correct is (1/3)^4 = 1/81, which is approximately 0.01235 when rounded to five decimal places.

(c) The probability of not getting any question correct is (2/3)^4, since there are two incorrect answers for each question and we are guessing on all four questions. Therefore, the probability of getting at least one question correct is 1 - (2/3)^4, which is approximately 0.51775 when rounded to five decimal places.

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Answer:

24 ...mm

Step-by-step explanation:

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Answer:

24 feet

Step-by-step explanation:

The area of a triangle is worked out by

Base x height x 1/2

8 x 6 = 48

48/2= 24

Hope that helped :)

The Lagrangian for maximizing Will's utility subject to his budget constraint can be written as the correct answer is A. L = xy^4 - λ(12x + 11y - 118).

The Lagrangian for maximizing Will's utility subject to his budget constraint can be written as

L = xy^4 - λ(p_x*x + p_y*y - m),

where x and y are goods, p_x and p_y are the prices of goods x and y respectively, and m is income.
In this case, Will has a Cobb-Douglas utility function, xy^4. His income is $118, the price of x is $12, and the price of y is $11.
To find the Lagrangian for maximizing Will's utility, we substitute the values into the equation:
L = xy^4 - λ(12x + 11y - 118).
Therefore, the correct answer is A. L = xy^4 - λ(12x + 11y - 118).

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Answer:

f(x) = -1

Step-by-step explanation:

f(x) = 5-3x

Put x = 2

f(x) = 5-3(2)

f(x) = 5-6

f(x) = -1

Answer:-1

Step-by-step explanation:

f(2)=5-3(2)

f(2)=5-6

f(2)=-1

4 cups of mayonnaise should be used if 1 cup of pecans is used.

As per the given data:

A recipe calls for  \($1\frac{1}{2}\) cups of mayonnaise and \($\frac{3}{8}\) cups of pecans.

First, convert the mixed fraction to an improper fraction.

\($1\frac{1}{2}\) cups of mayonnaise = \($\frac{3}{2}\)

Here we have to determine how much mayonnaise should be used if 1 cup of pecans is used.

This can be determined by using the unitary method.

We may determine the value of one unit from the value of many units and the value of many units from the value of one unit using the unitary technique.

The ratio of the amount of pecans comparing reality and the recipe is:

\($= \frac{1}{\frac{3}{8} }\)

= \($\frac{8}{3}\)

To find the amount of mayonnaise that should be added:

= \($\frac{8}{3}\) × \($\frac{3}{2}\)

= 4

Therefore 4 cups of mayonnaise is required.

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Age will be 40 years old.

R, in beats per minute, can be approximated by the formulas, where a represents the person's age.

where R= 143 - 0.65a for women.... (1)

and R= 165 - 0.75a for men,..... (2)

So by implementing these two equation we get a = 40

If the sum of ages is X and Y, and the ratio of their ages is p:q, then the age of Y can be calculated using the formula shown below: Y's age = Y's ratio/Sum of ratios x sum of ages The age dependency ratio is the ratio of dependents (people under the age of 15 or over the age of 64) to the working-age population (people between the ages of 15 and 64). The proportion of dependents per 100 working-age population is shown in the data.

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we have that

Let

y ----> total charge

x ----> number of hours

so

First-rate

y=65x+400 ------> equation 1

Second rate

y=95x+100 ------> equation 2

Equate equation 1 and equation 2

65x+400=95x+100

solve for x

95x-65x=400-100

30x=300

x=10 hours

therefore

the answer is

The average rate of change for the function f(x) = 2 cos(x^2) on the interval [1, 3] is approximately -0.198.

The formula for an average rate of change is (f(b) - f(a))/(b - a), where a and b are the endpoints of the interval. Plugging in the values, we get (f(3) - f(1))/(3 - 1) = (2cos(9) - 2cos(1))/(2) = -0.198. Therefore, the average rate of change for the function f(x) on the interval [1,3] is approximately -0.198.

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Answer:

D. P(10|blue)

Step-by-step explanation:

The correct expression for the probability of selecting a blue piece of paper given that it has the number 10 on it is:

C. P(blue|10)

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Here, "blue|10" means "blue given 10," which represents the conditional probability of selecting a blue paper given that the selected paper has the number 10 on it.

The formula for conditional probability is:

P(A|B) = P(A and B) / P(B)

In this case, A represents the event of selecting a blue piece of paper and B represents the event of selecting a paper with the number 10 on it.

We know that there are 10 blue pieces of paper and each color has 10 numbered pieces, so the total number of papers is 10+10+10=30.

Thus, the probability of selecting a paper with the number 10 on it is:

P(B) = 3/30 = 1/10

Out of the 10 blue pieces of paper, only one has the number 10 on it. Thus, the probability of selecting a blue piece of paper given that it has the number 10 on it is:

P(A and B) = 1/30

Therefore, the probability of selecting a blue piece of paper given that it has a number 10 on it is:

P(blue|10) = P(A and B) / P(B) = (1/30) / (1/10) = 1/3

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A line will have a positive slope if it makes an acute angle with a positive x-axis while if it makes an obtuse then the slope will be negative thus point (x₁,y₁) can be (2,5) and (x₂,y₂) could be (-7,5).

A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.

The slope is also calculated by differentiation for example slope of y = sinx will be y' = cosx.

A line will have a positive slope if it makes an acute angle with a positive x-axis while if it makes an obtuse then the slope will be negative.

As shown below,

The purple line makes an acute angle (less than 90 °) thus slope will be positive and the blue line makes an obtuse angle (greater than 90°) thus the slope is negative.

Hence "point (x₁,y₁) can be (2,5) and (x₂,y₂) could be (-7,5)".

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The area of a square and the two quarter circle is 369.04 square in

A composite shape can be defines as a shape created with two or more basic shapes. We often refer to composite shapes as compound and complex shapes as well.

The composite shape here involve a square and two quarter circle and two quarter circle gives a semi circle.

The area of a semi circle is ½πr²

The area of square is l²

The radius of the circle =l/2 = 16/2 = 8

Therefore the area of the composite shape = ½πr²+ l²

= ½×3.14×8² + 16²

= 113.04 + 256

= 369.04 square in

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Answer:

20 ÷ (2+2) x\(2^{2}\) + 6 = 26

Step-by-step explanation:

The circumference of the circle to the nearest hundredth is 21.98 inches.

The circumference of a circle is the measure of the boundary or the length of the complete arc of a circle.

The circumference of a circle is the perimeter of the circle. It's the wholes boundary of the circle.

The circumference of the circle can be found as follows:

circumference of a circle = 2πr

where

Therefore,

diameter of the circle = 7 inches

radius of the circle = 7 / 2 = 3.5 inches

Hence,

circumference of a circle = 2 × 3.14 × 3.5

circumference of a circle = 21.98 inches

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Answer:

24 slices

Step-by-step explanation:

There are 3 whole pizzas. He cuts each of them into eighths. That means eight slices. 3 times 8 is 24. There are a total of 24 slices. This can also look like this: 24/8   or 24 over 8.  Which also equals to 3.

Answer:

$27,444.80

Step-by-step explanation:

12% of 22,540 is 2,704.8

add the amount she made

add the weekly salary (550 × 4)

This system of inequalities represents is x² + y² ≤ 49 and 2x² < y

Inequality is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.

Let the numbers x and y,

According to 1st condition,

The sum of the squares of two different numbers is less than or equal to 49 :

x² + y² ≤ 49

According to 2nd condition,

Twice one of the numbers squared is less than the other number :

2x² < y

Hence, this system of inequalities represents is x² + y² ≤ 49 and 2x² < y

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Answer:

\(x\leq -2\)

Step-by-step explanation:

Solve for x:

\(-4x+20\geq 28\)

Subtract 20 on both sides

\(-4x\geq 8\)

Flip the sign and multiply both sides by -4

\(16x\leq -32\)

Divide by 16

\(x\leq -2\)

Answer:

Step-by-step explanation:

\(OA = 13, AS=\frac{1}{2}AC=6\)

Then

\(OS^2=OA^2-AS^2=13^2-6^2=169-36=133.\)

Now

\(SB=OB-OS=13-\sqrt{133}\)

Answer:

6.4m

Step-by-step explanation:

\( \frac{4 \\ }{5} \times 8 = \)

\( \frac{32}{5} \)

\( = 6 \frac{2}{5} \: or \: 6.4\)

Answer:

The market is 10 m from the girl's house.

Step-by-step explanation:

If a girl walked 8 m from her house to market and she covered 4/5 of the distance the market, then 8 m equals 4/5ths of the total distance from her house to the market.

Let x be the total distance from the girl's house to the market.

Create an equation with the given information and defined variable:

\(\implies \dfrac{4}{5}x=8\)

Multiply both sides of the equation by 5:

\(\implies 5 \cdot \dfrac{4}{5}x=5 \cdot 8\)

\(\implies 4x=40\)

Divide both sides of the equation by 4:

\(\implies \dfrac{4x}{4}=\dfrac{40}{4}\)

\(\implies x=10\)

Therefore, the market is 10 m from the girl's house.

The expression which represents how much money all three women make together, given they work the same number of weeks is (1,650w + 200)

Total amount all three women make together = (450w + 100) + (450w + 100) + (750w)

= 450w + 100 + 450w + 100 + 750w

= 1,650w + 200

So therefore, the total amount made by the three women is given by the expression 1,650w + 200

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Answer:

The answer is c

Step-by-step explanation:

Answer: 4.5 pounds

Explanation: To convert 72 ounces into pounds, we use the conversion factor for ounces and pounds which is 16 ounces = 1 pound.

Next, notice that we're going from a smaller unit, ounces, to a larger unit, pounds and when we go from a smaller unit to a larger unit, we divide. So here, we divide 72 by the conversion factor, 16, to get 4.5.

So 72 ounces equals 4.5 pounds.

Answer:

B

Step-by-step explanation:

i. The null and alternate hypotheses  H0: p = % of older adults, H1: p > older adults

II The Z-distribution is used to conduct a Z-test

iii The p value is 0.0014

iv. We reject the null hypothesis.

v. We can conclude that the population mean percentage of young adults who attended college is statistically significantly higher

i. H0: μ1 = μ2

H1: μ1 > μ2

The level of significance is α = 0.05.

ii. Because we are comparing two means, we will use the Z-distribution to conduct a Z-test. This is because we know the standard deviations from previous studies, and the sample size is large.

iii. To calculate the P-value, first, we calculate the Z score.

Z = (19.7 - 15.2) / √[(7.2² / 32) + (5.2² / 35)]

= 4.5 / √[(51.84 / 32) + (27.04 / 35)]

= 4.5 / √[1.620 + 0.772]

= 4.5 / 1.511

= 2.976

The P-value is the probability of observing a Z score as extreme as 2.976 or more under the null hypothesis.

This is found to be approximately 0.0014.

iv. Our P-value (0.0014) < (0.05).

we reject the null hypothesis.

v. We can conclude that the population mean percentage of young adults who attended college is statistically significantly higher than the population mean percentage of older adults who attended college at the 0.05 significance level.

b.The confidence interval can be calculated as:

(19.7 - 15.2) ± 1.645 * √[(7.2² / 32) + (5.2² / 35)]

= 4.5 ± 1.645 * 1.511

= 4.5 ± 2.484

= [2.016, 6.984]

So, we are 90% confident that the true difference in population mean percentages of young adults and older adults who attended college is between 2.016% and 6.984%.

This confidence interval tells us that, if we were to take many samples and compute a 90% confidence interval for each

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