I have no clue of how to solve this question below.

Answer:

a = -3

Step-by-step explanation:

Step 1:  Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:

5^a = 1/125

Step 2:  Take the log of both sides

log(5^a) = log(1/125)

Step 3:  According to the power rule of logs, we can bring a down and multiply it by log(5):

a * log(5) = log (1/125)

Step 4:  Divide both sides by log(5) to solve for a:

(a * log(5) = log(1/125)) / log(5)

a = -3

Optional 5:  We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:

5^-3 = 1/125

1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator

1/125 = 1/125

Answer: t = 7°

Step-by-step explanation:

        We know that a straight line is equal to 180 degrees and that the little box represents 90 degrees. Using this information we can create an equation to solve for t.

   Given:

180° = 90° + 6t° + 6° + 7t° - 7°

   Combine like terms:

180° = 89° + 13t°

   Subtract 89 from both sides of the equation:

91° = 13t°

   Divide both sides of the equation by 13:

t = 7°

Answer:

x = 3 , y = 1

Step-by-step explanation:

[tex]2^{x+y} = 16\\2^{x+y} = 2^4\\x + y = 4 ---- (1)\\\\3^{x-y} = 9\\3^{x-y} = 3^2\\x-y = 2 ----- (2)\\\\Adding 1 and 2 , we get ,\\ 2x = 6\\x = 3\\y = 1[/tex]

Answer:

y = 1, x = 3

Step-by-step explanation:

1.) Based on the given, we have [tex]2^{x+y}[/tex] = 16, and [tex]3^{x-y}[/tex]=9. Since [tex]2^4[/tex] is equal to 16, that means that x + y = 4. Since [tex]3^2[/tex] is equal to 9, that means that x - y = 2

2.) Now, we have a system of equations. By using elimination (adding the two together), you get x + x + y - y = 2 + 4. By simplifying, the y cancels out and you get 2x = 6. Finally, you get x = 3.

3.) To end, you need to find y. Since we have x - y = 2, and x = 3, that means that 3 - y = 2, meaning y = 1.

In a multiple regression model, the variance of the error term e is assumed to be the same for all values of the independent variable. Therefore, the correct option is C) the same for all values of the independent variable.

In multiple regression, we use several independent variables to predict the values of the dependent variable. The model estimates the relationship between the independent variables and the dependent variable by calculating the coefficients of the independent variables.

The error term e represents the difference between the predicted value of the dependent variable and the actual value of the dependent variable.

The assumption of constant variance of the error term e is known as homoscedasticity. It means that the variance of the errors is the same for all levels of the independent variables.

This assumption is important because, if the errors have different variances across the levels of the independent variable, the model may not accurately capture the relationship between the independent variables and the dependent variable, leading to biased and unreliable results. so, the correct answer is C).

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Therefore, the value of fy at (4, 1) is (sin⁻¹(4) + 4/√(-60)) / 8, or approximately -0.105 for given partial derivatives.

To find fy, we need to take the partial derivative of f with respect to y, treating x as a constant. Using the chain rule, we get:

f(x, y) = y sin⁻¹(xy)

∂f/∂y = sin⁻¹(xy) + y(1/√(1 - x²y²))(x)

Now we can substitute the given values of x and y to get:

∂f/∂y (4, 1) = sin⁻¹(4) + 1(1/√(1 - 16))(4)

= sin⁻¹(4) + 4/√(-60)

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Answer: $34.20

Step-by-step explanation:

$3.80 is for 1 book.

Since she would buy 9 books, you would do the equation of 3.80 x 9.

You'll get the answer of 34.2, but then by making that a dollar amount it would be 34.20. Add the dollar sign, $34.20, and wahlah!

Answer:The given expression is 6 - 8x + 3.

Combining like terms, we have:

6 - 8x + 3 = 9 - 8x

Therefore, the simplified expression is 9 - 8x.

Step-by-step explanation:

THANKS

To calculate the incidence of breast cancer in the unexposed group (i0) per 1,000, we need to first calculate the total number of mothers in the unexposed group. The total number of mothers in the study is 1,628 + 4,450 = 6,078.
We know that among the 4,450 mothers who first gave birth before the age of 30, 65 subsequently developed breast cancer.

Therefore, the incidence of breast cancer in this group is 65/4,450 = 0.0146.

To convert this incidence rate to a per 1,000 basis, we multiply by 1,000: 0.0146 x 1,000 = 14.6.

Therefore, the incidence of breast cancer in the unexposed group (i0) per 1,000 is 14.6.

It's important to note that we cannot directly calculate the incidence rate of breast cancer in the exposed group since we do not have information on the total number of mothers in that group who did not develop breast cancer. However, we can still compare the incidence rates between the exposed and unexposed groups to see if there is a significant difference.

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The complement set of S is {1, 3, 5, 8, 9, 10}.

To find the complement set of S, we need to identify all the elements in the universal set U that are not present in set S.

Given:

Universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Set S = {2, 4, 6, 7}

The complement set of S, denoted as S', consists of all the elements in U that are not in S.

Complement set of S (S') = U - S

To find S', we subtract the elements of S from U:

S' = {1, 3, 5, 8, 9, 10}

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To use the normal approximation for a test of two proportions, n1 p1, n1 (1 - p1), n2 p2, and n2 (1 - p2) must all be greater than or equal to 5.

This is because the normal distribution assumes that the sample size is large enough to approximate the binomial distribution, and the rule of thumb is that each cell (n1 p1, n1 (1 - p1), n2 p2, and n2 (1 - p2)) should have at least 5 expected counts. If any of these cells have fewer than 5 expected counts, then the normal approximation is not reliable and a more appropriate test should be used. It is important to note that this is just a rule of thumb, and other factors such as the size of the effect and the desired level of significance should also be considered when deciding on a statistical test.

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Answer:

missing length= 2.8

Step-by-step explanation:

a^2+b^2=c^2

a^2+1^2=3^2

a^2=3^2-1^2

a^2=8

a=2.8284271247461

a=2.8

The statement is False" Some seventh graders" isn't a set.

we know, set is a well- defined collection of distinct objects, which are appertained to as rudiments or members of the set.

For illustration, consider the set A = { 1, 2, 3}. This set contains the rudiments 1, 2, and 3.

It's a expression that describes a group of individualities without furnishing a well- defined collection of rudiments.

A set is a well- defined collection of distinct objects.

To represent a set, we generally use curled braces and list the rudiments within the set.

For illustration,{ 1, 2, 3} is a set containing the rudiments 1, 2, and 3.

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Answer:

-------------------------

Given data:

Put the data in the ascending order:

The mode, the most repeated term, is 11.

The median is the middle term, also 11.

The mean is the average:

Answer & step-by-step explanation:

Let us find the median of the data set

First, you should arrange the data in ascending to descending to find the median.

4, 7, 10, 11, 11, 12, 16

Now let us use the given formula to find the median.

[tex]\sf \dfrac{n+1}{2} =--^t^h data[/tex]

Here,

n → the number of elements

Let us find it now.

[tex]\sf Median= \dfrac{n+1}{2}\\\\\sf Median=\dfrac{7+1}{2} =4^t^h data\\\\Median=11[/tex]

Let us find the mode of the data set.

Mode is the most frequent number in the data set.

∴ mode → 11

Let us find the mean of the data set

Mean is the average of a data set.

To find that, you have to add all the data together and divide it by number of elements.

Mean = Σx ÷ n

Mean = ( 10 + 11 + 4 + 7 + 12 + 11 + 16 ) ÷ 7

Mean =  71 ÷ 7

Mean =  10.14

Answer: it would be 13 beeps

Step-by-step explanation:

The relationships between the line segments in the diagrams are as follows:

a) Equal Length

b) Parallel

c) Perpendicular

d) Equal Length

Let's analyze each diagram and determine the relationships between the line segments.

a) Equal Length:

In this diagram, the two line segments appear to be of the same length. They do not appear to be parallel or perpendicular to each other. When the lengths of two line segments are equal and their orientation doesn't affect this equality, we say they are of equal length. In this case, both line segments simply share the same length without any specific angle relationship.

b) Parallel:

In this diagram, the two line segments run side by side in the same direction and do not intersect. When two lines follow this pattern, they are considered parallel. Parallel lines have the same slope, which means they maintain a constant distance between each other as they extend indefinitely.

c) Perpendicular:

In this diagram, the two line segments meet at a right angle, forming a perfect 90-degree angle where they intersect. When two lines intersect at a right angle, they are referred to as perpendicular. Perpendicular lines have slopes that are negative reciprocals of each other, meaning they intersect at right angles.

d) Equal Length:

Similar to the first diagram, in this case, the two line segments are of equal length. They are not parallel or perpendicular; they simply have the same length.

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Answer:

$38.80

Step-by-step explanation:

part A.

The equation of the ellipse is:

x² / 280900 + y² / 198025 = 1

part B.

The area of the ellipse at the White House is found to be  741,022.16 square feet.

The standard form equation for an ellipse is given as :

(x² / a²) + (y² / b²) = 1

Where "a" =  half the length of the major axis

b =   half the length of the minor axis.

length of the major axis = 1060 feet,

a = 1060 / 2 = 530 feet.

The length of the minor axis is 890 feet,

b = 890 / 2

b= 445 feet.

x² / 530² + y² / 445² = 1

x² / 280900 + y² / 198025 = 1

B.

a = 530 feet and b = 445 feet.

Area = π * 530 * 445

A = 741,022.16 square feet

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it's the second answer 2 and 3 are same side interior angles

The equation of the composite function B(d) is B(d) = T(d) - A(d) or B(d) = d² + 8d

From the question, we have the following parameters that can be used in our computation:

T(d) = d² + 20d

A(d) = 12d

The function B(d) is the difference between the functions A(d) and T(d)

Using the above as a guide, we have the following:

B(d) = T(d) - A(d)

In terms of d, we have

B(d) = d² + 20d - 12d

Evaluate the difference

B(d) = d² + 8d

Hence, the composite function B(d) is B(d) = T(d) - A(d) or B(d) = d² + 8d

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Based on the evaluation of the conditions, the output "x < 0 and z > 0" will be printed. Therefore, the correct answer is B. x < 0 and z > 0.

The correct indentation of the statement would be as follows:

if (x > 0)

if (y > 0)

System.out.println("x > 0 and y > 0");

else if (z > 0)

System.out.println("x < 0 and z > 0");

Given that x = 1, y = -1, and z = 1, let's evaluate the conditions:

The first if statement checks if x > 0, which is true since x = 1.

Since the condition in the first if statement is true, we move to the inner if statement, which checks if y > 0. However, y = -1, so this condition is false.

The inner if statement is followed by an else if statement that checks if z > 0. Since z = 1, this condition is true.

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The translation of the triangle, 2 units up and 3 units to the left, followed by a dilation by a scale factor of 4 about the origin, indicates;

The coordinates of the vertex B is; (-20, 0)

A dilation transformation is one in which the size of the pre-image is transformed to produce the image, which may be smaller or increased in size.

The coordinates of the vertices of the triangles are;

A(3, 3), B(-2, -2), and C(4, -4)

The translation applied to the triangle are;

Vertical translation = 2 units up

Horizontal translation = 3 units to the left

The scale factor of the dilation = 4

The center of dilation = The origin

Therefore, we get;

The transformation applied to the vertices are as follows;

A(3 - 3, 3 + 2), B(-2 - 3, -2 + 2), and C(4 - 3, -4 + 2), which produces the coordinate points;

A(0, 5), B(-5, 0), and C(1, -2)

The dilation by a scale factor of 4, with the center of dilation at the origin, therefore, produces;

4 × (0, 5) ⇒ A'(0, 20)

4 × (-5, 0) ⇒ B'(-20, 0)

4 × (1, -2) ⇒ C'(4, -8)

The vertex of the coordinate B are therefore; (-20, 0)

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Answer: 9 + 3r

Step-by-step explanation:

To reduce the number of terms we need to combine like terms

15 - (6-3r)

Distributive property (distribute the -1)

15 - 6 + 3r

9 + 3r

The company will use approximately 7 trucks.

to separate into two or more parts or pieces. : to separate into classes or categories. : cleave entry 2, part.

To calculate the number of trucks needed, divide the total number of bicycles by the number of bicycles that can fit in each truck:

328 bicycles / 50 bicycles per truck = 6.56 trucks.

Since you can't have a fraction of a truck, the company will need to round up to the nearest whole number. Therefore, the company will use 7 trucks to ship the 328 bicycles across the country.

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To determine which ordered pairs satisfy the equation 3x - 4y = 21, we can substitute the given x and y values into the equation and check if the equation holds true.

Let's check each ordered pair:

1. (-1, -6):

  Substituting x = -1 and y = -6 into the equation: 3(-1) - 4(-6) = 3 + 24 = 27, which is not equal to 21. Therefore, (-1, -6) is not a solution.

2. (7, 0):

  Substituting x = 7 and y = 0 into the equation: 3(7) - 4(0) = 21, which is equal to 21. Therefore, (7, 0) is a solution.

3. (-3, 3):

  Substituting x = -3 and y = 3 into the equation: 3(-3) - 4(3) = -9 - 12 = -21, which is not equal to 21. Therefore, (-3, 3) is not a solution.

4. (11, 3):

  Substituting x = 11 and y = 3 into the equation: 3(11) - 4(3) = 33 - 12 = 21, which is equal to 21. Therefore, (11, 3) is a solution.

Based on the calculations, the ordered pairs that are solutions to the equation 3x - 4y = 21 are (7, 0) and (11, 3).

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Answer: 67

Step-by-step explanation:

We see a pattern where we multiply the number we added by previously by two.

For example, from 5 to 7, it is 2.

From 7 to 11, we add by 4.

From 11 to 19, we add by 8.

From 19 to 35, we add by 16.

This means the next number would be 32, adding 35 by 32 gives us 67,

Answer:

  (c)  379.2 in²

Step-by-step explanation:

You want to know the total surface area of 6 cylinders of diameter 3.5 inches and height 4 inches.

The area of a cylinder in terms of diameter and height can be found by ...

  A = πd(d/2 +h)

The area of 6 cylinders with d=3.5 and h=4 is ...

  6A = 6π(3.5 in)(3.5 in/2 +4 in) ≈ 379.2 in²

The minimum wrap needed is 379.2 square inches.

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Check the picture below.

let's firstly find side "t"

[tex]\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = \sqrt{a^2+b^2-(2ab)\cos(C)} \\\\[-0.35em] ~\dotfill\\\\ t = \sqrt{18^2+46^2~-~2(18)(46)\cos(158^o)} \implies t = \sqrt{ 2440 - 1371168 \cos(158^o) } \\\\\\ t \approx \sqrt{ 2440 - (-1535.42) } \implies t \approx \sqrt{ 3975.42 } \implies t \approx 63.05 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{Law of Sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin( R )}{18}\approx\cfrac{\sin( 158^o )}{63.05}\implies 63.05\sin(R)\approx18\sin(158^o) \\\\\\ \sin(R)\approx\cfrac{18\sin(158^o)}{63.05} \implies R\approx\sin^{-1}\left( ~~ \cfrac{18\sin( 158^o)}{63.05} ~~\right)\implies \boxed{R\approx 6.14^o}[/tex]

Make sure your calculator is in Degree mode.

Obtuse-angled: This term refers to triangles with one angle greater than 90 degrees. The triangle in question has an angle of 100º, so it is obtuse-angled.