If (6, 1) is dilated by a scale factor of 3 the new point would be:
A(3,3)
B (18,3)
C (15,3)
D (9.4)

Answer:

( 3, -2 )

Step-by-step explanation:

3, -2 is on the line so it is a solution

the rest of the points aren't in the shaded area or on the line therefore they are not a solution

Have a great day! :)

Answer:

-2 1/8

Step-by-step explanation:

Answer:

119

Step-by-step explanation:

308 - 56 = 252

252/4 = 63

63 + 56 = 119

Hope this helps!

Answer:

let Alice seashells be X and Chloe's be Y

x + Y = 308.........i

3(X - 56) = Y.......... ii

simultaneous equation created

{X + Y = 308}

{3X - 168 = Y}

X + Y = 308

3X - Y = 168........by elimination method

4X + 0 = 476

X = 119

therefore.... Alice had 119 seashells at first

from eqn(i)...

X + Y = 308

119 + Y = 308

Y = 308 - 119

Y = 189

therefore.... Chloe had 189 seashells at first

Answer:

312

Step-by-step explanation:

25+.15x=71.80

-25         -25

.15x=46.8

46.8/.15

x=312

Answer:

312 miles

Step-by-step explanation:

you have to subtract 25 from 71.80 which equals 46.80

then you have to divide 0.15 from 71.80 which equals 312

The last expression finally simplifies to cot β + tan α using quotient identity in trigonometric identities.

We want to verify the trigonometric  identity;

cos (α - β)/(cos α sin β) = cot β + tan α

Now, according to trigonometric identities in mathematics, we know that;

cos (α - β) = (cos α cos β) + (sin α sin β)

Thus, plugging that back into our left hand side of the main question gives;

[(cos α cos β) + (sin α sin β)]/(cos α sin β)

Rewriting this expression by separating the denominator gives;

[(cos α cos β)/(cos α sin β)] + [(sin α sin β)]/(cos α sin β)

Using quotient identities, this can be simplified to;

cot β + tan α

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Step-by-step explanation:

there is something severely wrong with the problem definition.

when the Hypotenuse = 9, there is no 30-60-90 triangle with a leg = 6.

and when we are just focusing that this is a right-angled triangle with the Hypotenuse = 9, then 6 cannot be the longer leg.

it is also not clear what the solution is supposed to be. the 2nd leg ? the area ? the perimeter ? the height(s) ? ...

what ?

so, all I can do here is to show you why I said what I said :

30-60-90 triangle with Hypotenuse = 9

then the longer leg is opposite of the 60° angle and therefore sin(60)×9 = 7.794228634...

the shorter leg is opposite of the 30° angle and therefore sin(30)×9 = 0.5×9 = 4.5

a right-angled triangle with Hypotenuse = 9, one leg = 6 gives us per Pythagoras for the other leg

9² = 6² + leg²

81 = 36 + leg²

45 = leg²

leg = sqrt(45) = 6.708203932...

so, you see, as stated above, there is no leg with the length 6 in such a 30-60-90 triangle.

and in a more general right-angled triangle, if one leg = 6, then the other leg is actually longer.

therefore, there is everything wrong with the problem definition.

the answer is A: 146 ≤ 9c + 10

14. The trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. In the trigonometric equation 2(cos²θ - sin²θ) = 1, θ = 15°

A trigonometric equation is an equation that contains a trigonometric ration.

14. To find the value of (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°, we proceed as follows

Since we have the trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°,

We know that sin47° = sin(90 - 43°) = cos43°. So, substituting this into the equation, we have that

(sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = (cos43°/cos43°)² + (cos43°/cos43°)² - 4cos²45°

= 1² + 1² - 4cos²45°

We know that cos45° = 1/√2. So, we have

1² + 1² - 4cos²45° = 1² + 1² - 4(1/√2)²

= 1 + 1 + 4/2

= 2 + 2

= 4

So, (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. If 2(cos²θ - sin²θ) = 1 and θ is a positive acute angle, we need to find the value of θ. We proceed as follows

Since we have the trigonometric equation 2(cos²θ - sin²θ) = 1

We know that cos2θ = cos²θ - sin²θ. so, substituting this into the equation, we have that

2(cos²θ - sin²θ) = 1

2(cos2θ) = 1

cos2θ = 1/2

Taking inverse cosine, we have that

2θ = cos⁻¹(1/2)

2θ = 30°

θ = 30°/2

θ = 15°

So, θ = 15°

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Answer:

(a) Yes, the data suggest that females are more likely to graduate from high school than males.

(b) A 95% confidence interval for the difference in the graduation rates between females and males is [0.024, 0.404] .

Step-by-step explanation:

We are given that a survey of over 25,000 Americans aged between 18 and 24 years revealed the following: 88.1% of the 12,678 females and 84.9% of the 12,460 males had high school diplomas.

Let \(p_1\) = population proportion of females who had high school diplomas.

\(p_2\) = population proportion of males who had high school diplomas.

(a) So, Null Hypothesis, \(H_0\) : \(p_1\leq p_2\)    {means that females are less or equally likely to graduate from high school than males}

Alternate Hypothesis, \(H_A\) : \(p_1 > p_2\)     {means that females are more likely to graduate from high school than males}

The test statistics that will be used here is Two-sample z-test statistics for proportions;

                        T.S.  =    ~  N(0,1)

where, \(\hat p_1\) = sample proportion of females having high school diplomas = 88.1%

\(\hat p_2\) = sample proportion of males having high school diplomas = 84.9%

\(n_1\) = sample of females = 12,678

= sample of males = 12,460

So, the test statistics =  

                                    =  7.428  

The value of the standardized z-test statistic is 7.428.

Now, at a 5% level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is more than the critical value of z as 7.428 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that females are more likely to graduate from high school than males.

(b) Firstly, the pivotal quantity for finding the confidence interval for the difference in population proportion is given by;

                        P.Q.  =  \(\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }\)  ~  N(0,1)

where, \(\hat p_1\) = sample proportion of females having high school diplomas = 88.1%

\(\hat p_2\) = sample proportion of males having high school diplomas = 84.9%

\(n_1\) = sample of females = 12,678

\(n_2\) = sample of males = 12,460

Here for constructing a 95% confidence interval we have used a Two-sample z-test statistics for proportions.

So, 95% confidence interval for the difference in population proportions, (\(p_1-p_2\)) is;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                      of significance are -1.96 & 1.96}    

P(-1.96 < \(\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }\) < 1.96) = 0.95  

P( \(-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }\) < \({(\hat p_1-\hat p_2)-(p_1-p_2)}\) < \(1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }\) ) = 0.95  

P( \((\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }\) < (\(p_1-p_2\)) < \((\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }\) ) = 0.95

95% confidence interval for (\(p_1-p_2\)) = [\((\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }\) , \((\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }\) ]

= [ \((0.881-0.849)-1.96 \times {\sqrt{\frac{0.881(1-0.881)}{12,678}+\frac{0.849(1-0.849)}{12,460}} }\) , \((0.881-0.849)+1.96 \times {\sqrt{\frac{0.881(1-0.881)}{12,678}+\frac{0.849(1-0.849)}{12,460}} }\) ]

= [0.024, 0.404]

Therefore, a 95% confidence interval for the difference in the graduation rates between females and males is [0.024, 0.404] .

(c) The assumptions and conditions necessary for the above inferences to hold are;

Answer:

D

Step-by-step explanation:

The answer is D because  a circle has at least a 360 degree and a 180 is a half circle.

Josh used 87 pounds of type B coffee in the blend.

What is equation?

An equation is a statement that two expressions are equal. It typically contains variables, which are quantities that can take on different values, and constants, which are quantities that have a fixed value. Equations can be used to describe relationships between different quantities and to solve problems by finding the values of variables that satisfy the equation.

For example, the equation 2x + 3 = 7 states that the expression 2x + 3 is equal to the expression 7.

Let's say that Josh used x pounds of type A coffee, and y pounds of type B coffee in the blend.

From the problem statement, we know that the total amount of coffee in the blend is 138 pounds, so x + y = 138.

The cost of the blend is $652.50, so 5.8x + 4.1y = 652.5.

We can use these two equations to solve for y, the number of pounds of type B coffee used.

First, we can solve for x in terms of y from the first equation,

x + y = 138

x = 138 - y

Then we can substitute this expression for x into the second equation,

5.8x + 4.1y = 652.5

5.8(138 - y) + 4.1y = 652.5

800.4 - 5.8y + 4.1y = 652.5

1.7y = 147.9

y = 87

Therefore, Josh used 87 pounds of type B coffee in the blend.

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Answer: x = 7/2

Step-by-step explanation: u juss simplify 1/2 x 7 to 7/2 so x = 7/2

The value of x in logarithmic equation \(log_{10}x(\frac{9}{63} )=\frac{1}{2}\) is \(1000\sqrt{10}\).

"A logarithmic equation is an equation that involves the logarithm of an expression containing a variable."

Given logarithmic equation

\(log_{10}x(\frac{9}{63} )=\frac{1}{2}\)

⇒ \(log_{10}x(\frac{1}{7} )=\frac{1}{2}\)

⇒ \(log_{10}x=\frac{1}{2}({7} )\)

⇒ \(log_{10}x=\frac{7}{2}\)

⇒ \(x = 10^{\frac{7}{2} }\)

⇒ \(x = 10^{3+\frac{1}{2} }\)

⇒ \(x = 10^{3}\) × \(10^{\frac{1}{2} }\)

⇒ \(x = 1000\sqrt{10}\)

The value of  \(x = 1000\sqrt{10}\)

Hence, the value of x in logarithmic equation \(log_{10}x(\frac{9}{63} )=\frac{1}{2}\) is \(1000\sqrt{10}\).

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The area of the forest after 13 years is  1990.08 \(km^2\).

What is exponential decay?

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b\()^x\), where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.

Here initial area a = 3500\(km^2\) ,

Rate of decay = 4.25%= 4.25/100 = 0.0425

Now using exponential decay formula then,

=> \(y=a(1-b)^x\) where x=13 years .

=> y = \(3500(1-0.0425)^{13}\)

=> y = \(3500(0.9575)^{13}\)

=> y = 1990.08 \(km^2\)

Hence the area of the forest after 13 years is  1990.08 \(km^2\).

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Answer:

By Pythagoras theorem

x² = 7² + 14²

x² = 49 + 196

x² = 245

X = square root of 245

245 is number that belongs to the green box

The missing side of the right triangle is √245. The number that belongs in the green box is 245

From the question, we are to determine the missing side of the given triangle

The missing side of the triangle can be determined by using Pythagoras' theorem

The theorem states that, in a right angle triangle

c² = a² + b²

Where c is the length of the longest side (hypotenuse)

and a & b are the other two sides

From the given information,

Hyp = x;

Let a = 7 and b = 14

∴ x² = 7² + 14²

x² = 49 + 196

x² = 245

x = √245

Heence, the missing side of the right triangle is √245. The number that belongs in the green box is 245.

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Answer:

31

Step-by-step explanation:

any number in the lines that's a negative will be positive.

Answer:

Exponential Function

General form of an exponential function with base \(e\):

\(f(x)=Ae^{kx}\)

where:

The curve crosses the y-axis at y = 40.  Therefore, A = 40.  

Substitute the found value of A into the formula along with (1, 56) and solve for \(k\):

\(\begin{aligned}f(x) & =Ae^{kx}\\\implies 56 & =(40)e^{k}\\e^k & =\dfrac{56}{40}\\k & =\ln (1.4)\end{aligned}\)

\(\textsf{Equation}: \quad f(x)=40e^{x\ln 1.4}\)

To find the population in 10 years, substitute \(x = 10\) into the found equation:

\(\begin{aligned}\implies f(10)&=40e^{10\ln 1.4}\\ & =1157.01862\\ & =1157\end{aligned}\)

The curve crosses the y-axis at y = 10.  Therefore, A = 10.

Substitute the found value of A into the formula along with (1, 18) and solve for \(k\):

\(\begin{aligned}f(x) & =Ae^{kx}\\\implies 18 & =(10)e^{k}\\e^k & =\dfrac{18}{10}\\k & =\ln (1.8)\end{aligned}\)

\(\textsf{Equation}: \quad f(x)=10e^{x\ln 1.8}\)

To find the population in 8 years, substitute \(x = 8\) into the found equation:

\(\begin{aligned}\implies f(8)&=10e^{8\ln 1.8}\\ & =1101.996058\\ & =1102\end{aligned}\)

Using the percentage concept, it is found that 60.29% of the people surveyed were completely satisfied with the car.

A percentage is the number of desired outcomes, multiplied by 100%, and divided by the number of total outcomes.

In this problem, researching in the internet, it is found that:

A total of 1260 + 650 + 180 = 2090 people were surveyed.

Of those, 1260 were completely satisfied.

Hence:

60.29% of the people surveyed were completely satisfied with the car.

refer to the attachment

thiz is called fraction!!

hope it helps...※※

Using midpoint of a line, the point at which E is located on the coordinates is (-4, -10)

Midpoint refers to a point that is in the middle of the line joining two points. The two reference points are the endpoints of a line, and the midpoint is lying in between the two points. The midpoint divides the line joining these two points into two equal halves. Further, if a line is drawn to bisect the line joining these two points, the line passes through the midpoint.

The formula of midpoint is given as

(x, y) = (x₂ + x₁) / 2 , (y₂ + y₁) / 2

Taking x-coordinate

x = (x₂ + x₁) / 2

2 = (8 + x₁) / 2

x₁ = -4

Taking the y - coordinate

y =  (y₂ + y₁) / 2

-4 = (2 + y₁) /2

y₁ = -10

The coordinate of E is (-4, -10)

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Answer:

3rd option: 32/24

Step-by-step explanation:

8/6 = 4/3

1st option: Now let's change the denominator to 24:

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

2nd option: Now let's change the numerator to 24:

4/3 ==> 24/?

4/3 =

4*6 / 3*6 = 24/18, not 24/32

24/32 = 3/4, not 4/3 ==> don't get confused by this

3rd option: 32/24 is correct [Look at the explanation for 1st option]

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

Hence, the 3rd option is correct.

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

6.11/104

Answer:0.03125

Step-by-step explanation:

GOO*OOGLE

Step-by-step explanation:

(1/2)^5   = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 =   1/32

Answer:

There are 8 pints to a gallon so she makes 120 gallons, and since she served 100 pints then there are 20 pints left over.

Brainliest please?

Answer:

There are 1.4 groups of 5/7 in 1.

Step-by-step explanation:

1 / (5/7)

An equation of the new graph is: A. y = ∣x - 4∣ - 9.

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) + N

Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:

y = ∣x - 4∣ - 9

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Missing information:

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

The value of e can be calculated by  e = A - f/2.

Usually, simplification involves proceeding with the pending operations in the expression.

For example, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.

Simplification usually involves making the expression simple and easy to use later.

We have been given an expression as;

A =e+f/2

We need to find the solution for 'e'.

So,

A = e+f/2

Subtract from f/2 on each side, we get;

A - f/2 = e

Thus, e = A - f/2

Therefore, the value of e can be calculated by  e = A - f/2.

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Answer:

C. Statistic because the value is a numerical measurement describing a characteristic of a sample

Answer:9a-2

Step-by-step explanation: see photo