Can someone show me how to work this problem?

The measure of the smallest angle in the triangle is 10.8°

An isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length.

The corresponding angles of the two equal lengths in an isosceles triangle are equal. This means that if we represent the two angles by x and the the third angle by y , then 2x+y = 180.

using cosine rule c² = a²+b²+2abcosC

a = 8, b = 8 and c = 3

3² = 8²+8²+2×8×8cos C

9 = 64+64+128cos C

128cosC = 9- 128

cos C = -119/128

cos C = -0.93

C = cos^-1 0.93

C = 158.4°

therefore 158.4 + A+ B = 180

A= B

2A = 180-158.4

2A = 21.6

A = 21.6/2

A = 10.8°

therefore A = B = 10.8°. This means the value of the smallest angle is 10.8°

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a. The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b. The probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c. Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

a) The three characteristics of this scenario that indicate we are working with Bernoulli trials are:

The experiment consists of a fixed number of trials (eight shots).

Each trial (shot) has two possible outcomes: hitting the target or missing the target.

The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b) To find the probability of hitting the 6th target (considered as a single trial), we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the binomial coefficient or number of ways to choose k successes out of n trials,

p is the probability of success in a single trial, and

n is the total number of trials.

In this case, k = 1 (hitting the target once), p = 0.88, and n = 1. Therefore, the probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c) To find the probability that the first time hitting the target is not until the 4th shot, we need to consider the complementary event. The complementary event is hitting the target before the 4th shot.

P(not hitting until the 4th shot) = P(hitting on the 4th shot or later) = 1 - P(hitting on or before the 3rd shot)

The probability of hitting on or before the 3rd shot is the sum of the probabilities of hitting on the 1st, 2nd, and 3rd shots:

P(hitting on or before the 3rd shot) = P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

Calculate these probabilities and sum them up to find P(hitting on or before the 3rd shot), and then subtract from 1 to find the desired probability.

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Answer:

9 is the answer

Step-by-step explanation:

if it was less then ten and not a multiple of 2 then i will ether be 1 3 5 7 9  but the composite numbers are 4 6 8 9 so since it is not a factor of 2 it has to be 9. so 9 is the answer

The number which is less than 10,  not a multiple of 2, and is a composite number, is 9.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical sizes.

Given:

I am less than 10 l am not a multiple of 2 l am a composite number,

The numbers which are less than ten are,

9, 8, 7, 6, 5, 4, 3, 2, 1, 0

The numbers which are not the multiple of 2 are shown below,

9, 7, 5, 3, 1, 0

The numbers which are composite are shown below,

9 = 3 × 3

Thus, The number is 9.

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Given:

Find: f(-2)

Explanation:

put x=-2 in the given equation.

Final answer: the required answer is

The given initial value problem is a second-order linear homogeneous differential equation. To solve it, we first find the characteristic equation by substituting y = e^(rx) into the equation. This leads to the characteristic equation r^2 - 10r + 50 = 0.

The general solution of the differential equation is y(x) = e^(5x)(C₁cos(5x) + C₂sin(5x)), where C₁ and C₂ are constants determined by the initial conditions.

To determine the particular solution, we differentiate y(x) to find y'(x) = e^(5x)(5C₁cos(5x) + 5C₂sin(5x) - C₂cos(5x) + C₁sin(5x)), and then differentiate y'(x) to find y''(x) = e^(5x)(-20C₁sin(5x) - 20C₂cos(5x) - 10C₂cos(5x) + 10C₁sin(5x)).

Substituting the initial conditions y(0) = 1 and y'(0) = 5 into the general solution and its derivative, we obtain the following equations:

1 = C₁,

5 = 5C₁ - C₂.

Solving these equations, we find C₁ = 1 and C₂ = 4.

Therefore, the particular solution to the initial value problem is y(x) = e^(5x)(cos(5x) + 4sin(5x)).

To find the value of y when x = 1.52, we substitute x = 1.52 into the particular solution and evaluate it. The result will depend on the rounding instructions provided.

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Answer:

Below.

Step-by-step explanation:

tan < XYZ = opposite/adjacent

= 8/20  = 0.4.

XYZ = 21.8 degrees to 3 s f.

Answer:

x=7+1/2

Step-by-step explanation:

 We move all terms to the left:

3(x+4.5)-(36.)=0

We add all the numbers together, and all the variables

3(x+4.5)-36=0

We multiply parentheses

3x+13.5-36=0

We add all the numbers together, and all the variables

3x-22.5=0

We move all terms containing x to the left, all other terms to the right

3x=22.5

x=22.5/3

x=7+1/2

Answer:

17 pieces

Step-by-step explanation:

The student use \(1\dfrac{1}{4}\) yards of paper for one box and \(\dfrac{7}{8}\) yard of paper for the other box.

Total no of rolls required is the sum of  \(1\dfrac{1}{4}\) yards and \(\dfrac{7}{8}\) yard. So,

\(S=1\dfrac{1}{4}+\dfrac{7}{8}\\\\=\dfrac{5}{4}+\dfrac{7}{8}\\\\=\dfrac{17}{8}\)

Let there are x no of pieces will the student cut to use for the gift boxes. It can be calculated as :

\(x=\dfrac{\dfrac{17}{8}}{\dfrac{1}{8}}\\\\=17\)

Hence, the student will cut 17 pieces to use the gift boxes.

The required results are following:

Step O : 1) Yes ,

2) Yes ; 3) No

step 1 : The null and alternative hypothesis are

H₀ : p = 0.105

Hₐ : p < 0.105

Step 2 : test statistic value is -0.865.

Step 3 : p- value is 0.1935 > 0.01 (α)

So, Fail to Reject null hypothesis and No, evidence to support that probability of births to mothers under 20 years of age is decreasing.

We have given that A sociologist claim that Births to mothers under 20 years of age is decreasing in United States.

Given data in statistics terms are

Sample size (n) = 134

Number of success = 11

level of significance , α = 0.01

hypothetical population proportion, p₀= 0.105

Step 0 :

1. Yes, this is a simple random sample because it fulfill all requirements.

2. Yes

np₀(1 - p₀) > 10

=> 134 x 0.105(1 – 0.105) > 10

=> 12.59265 > 10

3. No, as N is not given.

Step 1 :

The null and alternative hypothesis are

H₀: p = 0.105

Hₐ : p < 0.105

This is left-tailed hypothesis test.

Step 2:

The value of sample proportion (p-hat) = 11/134

The value of test statistic is

Z= (p-hat - p₀ )/√p₀(l-p₀)/n

Z = (11 /134 - 0.105)/√0.105(1-0.105) 134

Z= - 0.86512688616

Z = -0.865

Step 3 :

α =0.01 , Zα=-2.326

No, The test statistic does not lie in the rejection region

The P-value is

P-value= P(Z < z )

P-value= P(Z < -0.865 )

P-value= P(Z< -0.865)

P-value= 0.193519

P-value= 0.1935 > 0.01

Fails to Reject null hypothesis because P-value (0.1935) is greater than level of significance (0.01).

No, there is not sufficient evidence to conclude that the percentage of live births to mother under age 20 years of age in the United States has decreased below the 2006 level of 10.5%.

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Complete question:

In 2006, 10.5% of all live births in the United States were to mothers under 20 years of age. A sociologist claims that births to mothers under 20 years of age is decreasing. She conducts a simple random sample of 134 births and finds that 11 of them were to mothers under 20 years of age. Test the sociologist's claim at the a = 0.01 level of significance. Answer:

Step O: Verify Assumptions 1. Is this a simple random sample? (yes, no) 2. Is np. (1 - p.) > 10 ? (yes, no) 3. Is n < 0.05N? (yes, no)

Step 1: Parameter of interest: II.:P versus :p

Step 2: Test statistic: Sample Proportion= (Write your answer as a fraction without simplifying) Z. - (Use the value of the sample proportion as a fraction without simplifying in the formula of the test statistic and round your test statistic for three decimal places)

Step 3: Classical approach Z = (Rounded to three decimal places) Does the test statistic lie in the rejection region? (yes, no)

Step 4: p-value approach p-value= (Rounded to four decimal places) What is the relationship between p-value and a? p-value a. (>,<)

Step 5: Conclusion: Is there sufficient evidence to conclude that the percentage of live births to mothers under age 20 years of age in the United States has decreased below the 2006 level of 10.5%? (yes, no)

a. The market equilibrium price can be found by setting the quantity demanded equal to the quantity supplied. In this case, we have Pd = Ps, so we can set -10Qd + 80 = 2Qs + 20. Solving for Qs, we get Qs = (60 + 10Qd)/2.

b. To find the market equilibrium quantity, we substitute the value of Qs into the equation for Ps: Ps = 2Qs + 20. Plugging in the value of Qs, we get Ps = (60 + 10Qd)/2 + 20. Simplifying this equation, we find Ps = (30 + 5Qd) + 20, which simplifies further to Ps = 50 + 5Qd.

c. Consumer surplus represents the difference between the price consumers are willing to pay and the market equilibrium price. To calculate the consumer surplus, we need to find the area of the triangle above the market equilibrium quantity and below the demand curve. In this case, the demand curve equation is Pd = -10Qd + 80.

d. Producer surplus represents the difference between the market equilibrium price and the price producers are willing to sell at. To calculate the producer surplus, we need to find the area of the triangle below the market equilibrium quantity and above the supply curve. In this case, the supply curve equation is Ps = 2Qs + 20.

e. Total surplus is the sum of the consumer surplus and the producer surplus.

f. To graph the market, we can plot the demand and supply curves on a graph with price on the y-axis and quantity on the x-axis. We can label the equilibrium price and quantity as the point where the demand and supply curves intersect. The consumer surplus and producer surplus can be represented by shaded areas on the graph.

The specific values for the market equilibrium price, quantity, consumer surplus, producer surplus, and total surplus cannot be determined without additional information or values for Qd.

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Therefore, after answering the given query, we can state that With simple interest  a 5% rise per year, Beth's income in 14 years will be $69,394.38.

By dividing the base by the interest income, the time between payments, and many other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula for use in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating payment is as a portion of the principle amount. For example, if he takes $100 from a buddy and undertakes to pay back the loan at 5% interest, he only will pay his share of the 100% curiosity. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must collect interest when you give it. Typically, interest is determined as an indicator of the overall of the loan total. The loan's interest is the name given to this percentage.

The following is the compound interest formula:

A is equal to P(1 + r/n)(n*t), where A is the total sum.

P is equal to the starting principal.

the annual compound interest rate at the annual compound interest rate at the annual compound interest rate at the rate at the rate (as a decimal)

n represents how many times the interest is compounded annually.

t = the duration in years

The beginning wage (P) in this scenario is $37,000, the interest rate (r) is 5%, the number of times compounded (n) is 1 (since we're assuming the raise occurs once a year), and the number of years (t) is 14. This allows us to enter these values into the formula:

A =\($37,000(1 + 0.05/1)^(1*14)\)

A = $37,000(1.05)^14*A =  $69,394.38

With a 5% rise per year, Beth's income in 14 years will be $69,394.38.

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The total volume of vinegar in the four (4) largest samples is 14 fluid ounces.

In Mathematics and Statistics, a dot plot is a type of line plot that graphically represents a data set above a number line, through the use of crosses or dots.

Based on the information provided about the volume of vinegar that was used by each of the 17 students in their volcano experiment, we can reasonably infer and logically deduce that the four (4) largest sample is 3 1/2 fluid ounces.

Therefore, the total volume of vinegar in the four (4) largest samples can be calculated as follows;

Total volume of vinegar = 3 1/2 × 4

Total volume of vinegar = 7/2 × 4

Total volume of vinegar = 14 fluid ounces.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.

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The length of the base and the height of the triangle in feet are 16 feet and 6 feet respectively.

An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Let b represent the base of the triangle and h is the height, hence:

b = 2h + 4       (1)

Also, the area of the triangle is 48 square feet:

48 = (1/2)bh

96 = bh

(2h + 4)h = 96

2h² + 4h - 96 = 0

h = 6

b = 2(6) + 4 = 16

The length of the base and the height of the triangle in feet are 16 feet and 6 feet respectively.

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Answer:

\(-3(x+2)+5x=-9\\-3x-6+5x=-9\\-3x+5x=-9+6\\2x=-3\\x=-\frac{3}{2}\)

To find the probability that the mean weight of 19 fish is between 16.1 and 20.6 lb, you would need to know the distribution of the weights of the individual fish. If the weights of the fish are normally distributed with a mean of 18.4 lb and a standard deviation of 2.5 lb, then you can use a normal distribution to find the probability that the mean weight of the 19 fish falls in the specified range.

How does probability work exactly?

Probability is calculated by dividing the total possible outcomes by the number of outcomes that are theoretically possible. Probability differs from odds in this regard. Calculating odds involves dividing the likelihood of a particular event by the likelihood that it won't occur.

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Answer:

$65.00 total, $32.50 each

Step-by-step explanation:

We can model the cost of renting a canoe with the expression y = 25 + 5x, where x is the number of hours spent canoeing and y is the total cost.

Since Tommy and his friend spent 8 hours canoeing, we'll plug that in to x and solve.

y = 25 + 5(8)

y = 25 + 40

y = 65

This means the total cost of the trip is $65.

If they decide to split this cost between the two of them, they will each pay $32.50 as 65/2 = 32.5.

(a) The solutions for x* and y* are given by equations (6) and (7), respectively. (b) When I = $24, Pₓ = $4, and Pᵧ = $2, the optimal values of x* and y* are x* = 16 and y* = 20, respectively.

(a) To solve for x* and y* in terms of Pₓ, Pᵧ, and I, we need to find the utility-maximizing bundle that satisfies the budget constraint.

The utility function is given as U(x, y) = x^(1/2) * y^(1/2).

The budget constraint is expressed as Pₓ * x + Pᵧ * y = I.

To maximize utility, we can use the Lagrange multiplier method. We form the Lagrangian function L(x, y, λ) = U(x, y) - λ(Pₓ * x + Pᵧ * y - I).

Taking the partial derivatives of L with respect to x, y, and λ and setting them equal to zero, we get:

∂L/∂x = (1/2) *\(x^(-1/2) * y^(1/2)\)- λPₓ = 0   ... (1)

∂L/∂y = (1/2) *\(x^(1/2) * y^(-1/2)\) - λPᵧ = 0   ... (2)

∂L/∂λ = Pₓ * x + Pᵧ * y - I = 0               ... (3)

Solving equations (1) and (2) simultaneously, we find:

\(x^(-1/2) * y^(1/2)\)= 2λPₓ   ... (4)

\(x^(1/2) * y^(-1/2)\)= 2λPᵧ   ... (5)

Dividing equation (4) by equation (5), we have:

\((x^(-1/2) * y^(1/2)) / (x^(1/2) * y^(-1/2))\) = (2λPₓ) / (2λPᵧ)

y/x = Pₓ/Pᵧ

Substituting this into equation (3), we get:

Pₓ * x + (Pₓ/Pᵧ) * x - I = 0

x * (Pₓ + Pₓ/Pᵧ) = I

x * (1 + 1/Pᵧ) = I

x = I / (1 + 1/Pᵧ)        ... (6)

Similarly, substituting y/x = Pₓ/Pᵧ into equation (3), we get:

Pᵧ * y + (Pᵧ/Pₓ) * y - I = 0

y * (Pᵧ + Pᵧ/Pₓ) = I

y * (1 + 1/Pₓ) = I

y = I / (1 + 1/Pₓ)        ... (7)

Therefore, the solutions for x* and y* are given by equations (6) and (7), respectively.

(b) Given I = $24, Pₓ = $4, and Pᵧ = $2, we can substitute these values into equations (6) and (7) to find the values of x* and y*.

x* = 24 / (1 + 1/2) = 16

y* = 24 / (1 + 1/4) = 20

So, when I = $24, Pₓ = $4, and Pᵧ = $2, the optimal values of x* and y* are x* = 16 and y* = 20, respectively.

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Suppose U(x,y)=x  1/2  y  1/2  and P  x ​  x+P  y ​  y=I a. Solve for x  ∗  (P  x ​  ,P  y ​  ,I) and y  ∗  (P  x ​  ,P  y ​  ,I). b. What are the values of x  ∗  (P  x ​  ,P  y ​  ,I) and y  ∗  (P  x ​  ,P  y ​  ,I) if I=$24,P  x ​  =$4 and,P  y ​  =$2?

In the second market has the better deal the cost of one pound of apple is $1.79.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, at one market, Shawna finds apples selling for $1.89 a pound.

At another market she finds a 15-pound bag of apples for $26.99.

So, the cost of a pound of apple is 26.99/15

= $1.79

Therefore, in the second market has the better deal the cost of one pound of apple is $1.79.

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Answer:9

Step-by-step explanation:

Answer:

None of the above.

Step-by-step explanation:

The answer for this is -9, but on Khan academy the choices are-

x=-6

x=4

x=7

x= There is no such input value.

This is for Khan academy! Hope this helps!

Answer:

Step-by-step explanation:

It should be:

Answer:

D) (8,-22)

Step-by-step explanation:

I used my graphing calculator.

Answer:

D

Step-by-step explanation:

If the function be f(x) = 1.5 x² - 4 then the inverse of the function is \(f^{-1}\)(x) = 3x - 4

An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function " f " takes x to y, then its inverse will take y to x. The inverse function is denoted by f-1 or F-1 if the function is denoted by ' f ' or ' F '.

Let the given function be f(x) = 1.5 x² - 4

To find the inverse of the function

\(f^{-1}\)(x)

To differentiate f(x) with respect to x

\(f^{-1}\)(x) = 2x(1.5) - 4

simplifying the above equation, we get

\(f^{-1}\)(x) = 3x- 4

Therefore, the inverse of f(x) = 3x - 4

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Answer:

\(\boxed{\frac{25\pi }{36}}\)

Step-by-step explanation:

Use the formula to convert from degrees to radians: \(x * \frac{\pi }{180}\), where x is the value in degrees.

\(125 * \frac{\pi }{180}\) = \(\frac{125\pi }{180}\)

Then, simplify your fraction ⇒ \(\frac{125\pi }{180} = \boxed{\frac{25\pi}{36} }\)

(a) Relative frequency of No answers = 43/120

(b) Degrees in No portion = (43/120) * 360

To find the relative frequency of the Yes answers, divide the number of Yes answers (57) by the total sample size (120):

Relative frequency of Yes answers = 57/120

To find the number of degrees in the Yes portion of the pie chart, multiply this relative frequency by the number of degrees in a circle (360):

Degrees in Yes portion = (57/120) * 360

To find the relative frequency of the No answers, divide the number of No answers (43) by the total sample size (120):

Relative frequency of No answers = 43/120

The number of degrees in the section of the pie chart showing the No answers will be:

Degrees in No portion = (43/120) * 360

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Step-by-step explanation:

\( {x}^{2} = \frac{361}{100} \\ x = \sqrt{ \frac{361}{100} } = \frac{19}{10} = 1.9 \\ thank \: you\)

Answer:

$102.9

Step-by-step explanation:

20% of 85.73 is 17.15

to finish, you’ll just need to add 85.73 with 17.15 to get you answer,

the total cost of the meal is $102.9

brainliest? ..if you don’t mind

Answer:

$102.876 or $102.88

Step-by-step explanation:

20%/100=0.20

85.73*0.20=17.146

85.73+17.146=102.876

let other one be (x,y)

We know midpoint formula

\(\boxed{\sf (x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}\)

\(\\ \sf\longmapsto (6,-4)=\left(\dfrac{13+x}{2},\dfrac{-2+y}{2}\right)\)

\(\\ \sf\longmapsto \dfrac{13+x}{2}=6\)

\(\\ \sf\longmapsto 13+x=12\)

\(\\ \sf\longmapsto x=12-13\)

\(\\ \sf\longmapsto x=-1\)

And

\(\\ \sf\longmapsto \dfrac{-2+y}{2}=-4\)

\(\\ \sf\longmapsto -2+y=-8\)

\(\\ \sf\longmapsto y=-8+2\)

\(\\ \sf\longmapsto y=-6\)

Answer:

(- 1, - 6 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) ) ← midpoint formula

Use this formula on the endpoints and equate to the coordinates of the midpoint.

let the other endpoint = (x, y) , then

\(\frac{13+x}{2}\) = 6 ( multiply both sides by 2 )

13 + x = 12 ( subtract 13 from both sides )

x = - 1

\(\frac{-2+y}{2}\) = - 4 ( multiply both sides by 2 )

- 2 + y = - 8 ( add 2 to both sides )

y = - 6

The coordinates of the other endpoint are (- 1, - 6 )