Jen wants to have 8 rose bushes planted on her property. She asked a landscaping company to give her a bid. The contractor wanted $800 to buy and plant the bushes. Shell thinks she can do it by herself and save money. The bushes cost $60 each. How much will Jen save by planting the bushes herself? Write your answer using the $, such as $230

Answer:

A. Using the lens equation, 1/p + 1/q = 1/f, and substituting f = 5 cm and q = 7 cm, we can solve for p:

1/p + 1/7 = 1/5

Multiplying both sides by 35p, we get:

35 + 5p = 7p

Simplifying and rearranging, we get:

2p = 35

Therefore, the distance from the lens to the object, p, is:

p = 35/2 cm

B. Solving the lens equation, 1/p + 1/q = 1/f, for q, we get:

1/q = 1/f - 1/p

Substituting f = 5 cm, we get:

1/q = 1/5 - 1/p

Multiplying both sides by 5qp, we get:

5p = qp - 5q

Simplifying and rearranging, we get:

q = 5p / (p - 5)

Therefore, the expression that gives q as a function of p is:

q = 5p / (p - 5)

C. Here is a sketch of the graph of q(p):

The graph is a hyperbola with vertical asymptote at p = 5 and horizontal asymptote at q = 5. The image distance q is positive for object distances p greater than 5, which corresponds to a real image. The image distance q is negative for object distances p less than 5, which corresponds to a virtual image.

D. Taking the limit of q as p approaches infinity, we get:

lim q(p) = 5

This represents the horizontal asymptote of the graph. As the object distance becomes very large, the image distance approaches the focal length of the lens, which is 5 cm.

Taking the limit of q as p approaches 5 from the positive side, we get:

lim q(p) = -infinity

This represents the vertical asymptote of the graph. As the object distance approaches the focal length of the lens, the image distance becomes infinitely large, indicating that the lens is no longer able to form a real image.

In order for the lens to form a real image, the object distance p must be greater than the focal length f. When the object distance is less than the focal length, the lens forms a virtual image.

Answer:

Discrete random variable.

Step-by-step explanation:

Discrete variable:

Countable numbers(0,1,2,3,...)

Continuous variable:

Can assume decimal values, such as 0.5, 2.5,...

Number of bald eagles:

Number of bald eagles is a countable value, either there a 0, 100, 1000,... so it is a discrete random variable.

Answer:

Discrete random variable.

Step-by-step explanation:

Answer:

diffrence

Step-by-step explanation:

Using the concept of perimeter of polygon, the perimeter of figure C is 27cm shorter than total perimeter of A and B

To solve this problem, we have to know the perimeter of the polygon C.

The perimeter of a polygon is the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The perimeter of the figures are;

Using the concept of perimeter of a rectangle;

a. figure A = 2(4 + 11) = 30cm

b. figure B = 2(8 + 4) = 24cm

c figure C = 11 + 4 + 8 + 4 = 27cm

Now, we can add A and B and then subtract c from it.

30 + 24 - 27 = 27cm

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Answer:

∠ABC = 94°

∠BCD = 25°

∠ACB = 43°

Step-by-step explanation:

∠ABD = 133°

Since △ADC is an isosceles triangle where AD = CD, it means that ∠CBD = 133°

We know sum of angles at a point is 360°.

Thus; ∠ABC = 360 - (133 + 133)

∠ABC = 94°

Now, in △BCD, ∠B = 133° and ∠D = 22°

Sum of angles in a triangle = 180°

Thus; ∠BCD = 180 - (133 + 22)

∠BCD = 25°

Since the △ABC is also an isosceles triangle , it means that;

In △ABC, ∠A = ∠C

Thus; ∠ACB = (180 - 94)/2

∠ACB = 86/2

∠ACB = 43°

The expected length of the piece that we are left with after breaking twice is L/4 and the variance Var(X) is 7L^2/144.

In the given question, consider a stick of length 1.

We break it at a point which is chosen randomly and uniformly over its length and keep the piece that contains the left end of the stick.

We then repeat the same process on the piece that we were left with.

We have to find expected length of the piece that we are left with after breaking twice.

In the same setting as Q7, suppose the length of the piece that we are left with after breaking twice is Y.

We also have to calculate the variance Var(Y).

Following Laws are used in the solution

Law of Iterated Expectations: E[X] = E[ E[X|Y] ]

& Law of total variance: Var(X) = E[Var(X|Y)]+Var(E[X|Y])

Now, Y = Length of the stick after we break it the first time

and X = length of the stick after we break it the second time

As both the distribution is uniformly distributed.

Now, E[Y] = L/2 and Var(Y)= l^2/12

E(x|y)[X|Y=y] = y/2 and Var(x|y)[X|Y=y] = y^2/12

As the expectation of uniform distribution over {a,b} is (b-a)/2 and variance is (b-a)^2/12

Using Law of Iterated Expectations

E[X] = E[ E[X|Y] ]

E[X] = E[ y/2 ]

E[X] = \int_{L}^{0}

E[X] = L/4

Now using Law of Total Variance

Var(X) = E[Var(X|Y)]+Var( E[X|Y] )

Var(X) = E[y^2/12]+Var(y/2)

Var(X) = (1/12)*E[Y^2]+(1/4)*Var(Y)

Var(X) = (1*12)*(Var[Y] + (E[Y])^2) + (1/4)*Var(Y)

Var(X) = (1/12)*(L^2/12+L^2/4) + (1/4)*(L^2/12)

Var(X) = 7L^2/144

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The solution of the expression is x = -39.53.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

An expression,

12 + x = 0.70(20 + x).

Simplifying,

12 + x = 0.14 + 0.7x

x - 0.7x = 0.14 - 12

x = -39.53

And we have x = 6.67.

That is an incorrect assumption.

Therefore, x = -39.53.

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Answer:  7.5²π   square centimeters.  OR  56.25π cm²

Step-by-step explanation:

Circumference = diameter × π

So the diameter is 15 cm

Area = πr²

Radius is half the diameter, so 15/2 or 7.5

Area = (15/2)²π cm²  

Answer:

\(\displaystyle F(v) = \frac{9}{5}(v-273)+32\)

Step-by-step explanation:

The temperature T(d) in degrees Fahrenheit in terms of Celsius d is given by:

\(\displaystyle T(d)=\frac{9}{5}d+32\)

And the temperature C(v) in degrees Celsius in terms of Kelvin v is given by:

\(C(v)=v-273\)

We want the formula for the temperature F(v) in degrees Fahrenheit in terms of the Kelvin temperature.

So, we can use a composition of functions. Since T(d) outputs the temperature in Fahrenheit and C(v) inputs the temperature in Kelvin, T(C(v)) will be the temperature in Fahrenheit given the temperature in Kelvin. So:

\(\displaystyle T(C(v))=\frac{9}{5}(C(v)))+32\)

Substitute:

\(\displaystyle T(C(v)) = F(v) = \frac{9}{5}(v-273)+32\)

Therefore:

\(\displaystyle F(v) = \frac{9}{5}(v-273)+32\)

Answer:

(a)31.42 inches

(b)942.48 Square Inches

Step-by-step explanation:

Given a sector of a circle with the following dimensions:

Radius of the circle =60 inches

Central Angle of the sector =30°

(a)Arc Length

Arc Length \(=\dfrac{\theta}{360^\circ}X2\pi r\)

\(=\dfrac{30}{360^\circ}X2*60*\pi\\\\=10\pi\\\\=31.42$ Inches (correct to the nearest hundredth)\)

(b)Area of the sector

Area of the sector \(=\dfrac{\theta}{360^\circ}X\pi r^2\)

\(=\dfrac{30}{360^\circ}X\pi*60^2\\\\=300\pi\\\\=942.48$ Square Inches (correct to the nearest hundredth)\)

Answer:

(a)31.42 inches

(b)942.48 Square Inches

Step-by-step explanation:

Answer:

  x = 9 inches

Step-by-step explanation:

You want the value of x in the similar triangles shown.

Corresponding sides are proportional. This means the ratio of the horizontal side of the triangle to the vertical side is the same for both.

  6/4 = (6+x)/10

  15 = 6 +x . . . . . . . . multiply by 10

  9 = x . . . . . . . . . subtract 6

The measure of x is 9 inches.

__

Additional comment

You could also write the proportion ...

  6/4 = x/(10 -4)

  x = 36/4 = 9 . . . . . . . multiply by 6

You can see this if you draw a horizontal line through the figure at the top of the side marked 4 in.

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Answers:

=====================================================

Explanation:

A conditional statement is of the form "if..., then..."

For example, "If it rains, then the grass gets wet" is a conditional statement.

We can have a basic template of "If P, then Q" to represent any conditional. The P and Q are placeholders for logical statements.

The converse of that conditional is "If Q, then P". We swap P and Q.

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

So let's say we had this original conditional:

The converse would be:

Similar ideas apply for the other converses as well.

Answer:

If alternate interior angles are congruent, then lines are parallel.

If alternate exterior angles are congruent, then lines are parallel.

If corresponding angles are congruent, then lines are parallel.

If consecutive interior angles are supplementary, then lines are parallel.

If consecutive interior angles are supplementary, then lines are parallel.

Step-by-step explanation:

Converse

The converse of a statement is formed by switching the hypothesis and the conclusion.

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

Given statement:  If lines are parallel, then alternate interior angles are congruent.

Converse statement:  If alternate interior angles are congruent, then lines are parallel.

Given statement:  If lines are parallel, then alternate exterior angles are congruent.

Converse statement:  If alternate exterior angles are congruent, then lines are parallel.

Given statement:  If lines are parallel, then corresponding angles are congruent.

Converse statement:  If corresponding angles are congruent, then lines are parallel.

Given statement:  If lines are parallel, then consecutive interior angles are supplementary.

Converse statement:  If consecutive interior angles are supplementary, then lines are parallel.

Given statement:  If lines are parallel, then consecutive exterior angles are supplementary.

Converse statement:  If consecutive exterior angles are supplementary, then lines are parallel.

The measure of angle D is 45°

Similar triangles have the same corresponding angle measures and proportional side lengths. When two triangles are similar, the corresponding angles are equal.

And also the ratio of corresponding sides of similar triangles are equal.

To know the corresponding angles

side AC is corresponding to side EF, therefore angle D is congruent to angle A

angle D = 45°

OR , we can use the sum of angles In a triangle , which is 180°

angle D = 180 -( 72+63)

= 180 - 135

= 45°

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Answer:

\(x=-5,-1,1,5\)

Step-by-step explanation:

Use the Zero Product Property and set each factor equal to 0

\(h(x)=5(x-5)(x+5)^2(x^2-1)\)

\(0=x-5\\x=5\)

\(0=(x+5)^2\\0=x+5\\x=-5\)<-- Multiplicity of 2

\(0=x^2-1\\0=(x-1)(x+1)\\x=-1,1\)

Therefore, all real zeroes of the function are \(x=-5,-1,1,5\)

The correct answer is March, as it was the month in which the average number of hours worked by the website designers was closest to 50 hours.

A month is a unit of time typically consisting of 30 or 31 days. It is used for measuring periods of time, for example, when we say something happened "a month ago". Months are used in both the Gregorian calendar and the Julian calendar.

This data was gathered from a survey of website designers, which was conducted to determine the average number of hours each month that these professionals spent working.

In January, the average number of hours worked was 46.5. In February, it was 48.8. However, in March, the average number of hours worked was 49.4, which was the closest to 50 hours. This was followed by April, in which the average was 49.7.

Overall, it can be concluded that March was the month in which the average number of hours worked by website designers was closest to 50 hours. This is important data for website designers, as it allows them to understand the amount of time they should be spending on their work in order to be successful. It also helps employers gauge the workload of their website designers and ensure they are providing an adequate amount of work.

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The Volume of each bead is approximately 1.767 mm^3 when rounded to the nearest tenth.

The volume of each bead, the volume of a sphere using its diameter. The formula for the volume of a sphere is given by:

V = (4/3) * π * r^3

where V is the volume and r is the radius of the sphere.

Given that the diameter of each bead is 1.5 millimeters, we can calculate the radius as half of the diameter:

r = 1.5 mm / 2 = 0.75 mm

Now, we can substitute the value of the radius into the volume formula:

V = (4/3) * π * (0.75 mm)^3

Using the value of π ≈ 3.14 and performing the calculations:

V ≈ (4/3) * 3.14 * (0.75 mm)^3

V ≈ (4/3) * 3.14 * 0.421875 mm^3

V ≈ 1.767 mm^3 (rounded to the nearest tenth)

the volume of each bead is approximately 1.767 mm^3 when rounded to the nearest tenth.

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Answer:

A, C, D

Step-by-step explanation: the side of the > that has the opening is the side that should have the greater number, so if its like answer A its true

Answer:

3

Step-by-step explanation:

20÷100=0.2

0.2×15=3

:)

Answer:

Lin's father would pay $17 for his meal.

Step-by-step explanation:

15*20 = 300

300/100 = 3

20 - 3 = 17

Answer:

Quantity = 5 grapes

Step-by-step explanation:

Given the following data;

Quantity of grapes = 20

Cost = 48

To find the cost of each grape;

Cost of each grape = total cost/quantity

Cost of each grape = 48/20

Cost of each grape = $2.4

Now, to find how many grapes $12 can buy;

Quantity = total cost/cost of each grapes

Quantity = 12/2.4

Quantity = 5 grapes

Therefore, $12 can buy 5 grapes.

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

What is congruent?

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

Here,

we have to prove when can we say that the two triangles are congruent.

SSS, SAS, ASA, AAS, and HL.

These tests describe combinations of congruent sides and/or angles that are used to determine if two triangles are congruent.

Hence, two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

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Answer:

1.6875

Step-by-step explanation:

Volume of a pyramid = 1/3 (l*w*h)

Volume = 1/3(6 * 6 * 9)

Volume = 2 * 6 * 9

Volume = 108 cm³

Volume of cube = s³ ; s = side length

Volume = 4³ = 4 * 4 * 4 = 64 cm³

Number of wax cube = Volume of pyramid / volume of cube

= 108 cm³ / 64 cm³

= 1.6875

percentage EXPLANATION

Let's calculate the percentaje:

With a weekly budget of $12, Mark will need to save money for 9 weeks, 5 days in order to purchase the guitar.

The value is said to be in its simplified form when divided through its smallest equivalent fraction. How to find the most basic form. Find common factors in the denominator and numerators. Verify a minority integer t verify if it qualifies like a prime number. A statement comprising two rotational symmetry and an equal sign in the middle is called an equation in mathematics. The general form of almost any equation contains the degrees of all variables in descending order. The conventional form of something like a linear equation is an x + b = 0. The general form of a mathematical expression with two variables is an x + b y + c = 0. (or something similar). Equations can be categorized as identities or conditional solutions. An identity holds true irrespective of the value given to the variables.

given

let the week be x

equation =  $55 + 12x = $169.00

55 + 12x = 169

12x = 169 - 55

12x = 114

x = 9.5

With a weekly budget of $12, Mark will need to save money for 9 weeks, 5 days in order to purchase the guitar.

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Answer:

The minimum sample size needed is \(n = (\frac{1.96\sqrt{\sigma}}{4})^2\). If n is a decimal number, it is rounded up to the next integer. \(\sigma\) is the standard deviation of the population.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.9}{2} = 0.05\)

Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.05 = 0.95\), so Z = 1.645.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

How large a sample must she select if she desires to be 90% confident that her estimate is within 4 ounces of the true mean?

A sample of n is needed, and n is found when M = 4. So

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(4 = 1.96\frac{\sigma}{\sqrt{n}}\)

\(4\sqrt{n} = 1.96\sqrt{\sigma}\)

\(\sqrt{n} = \frac{1.96\sqrt{\sigma}}{4}\)

\((\sqrt{n})^2 = (\frac{1.96\sqrt{\sigma}}{4})^2\)

\(n = (\frac{1.96\sqrt{\sigma}}{4})^2\)

The minimum sample size needed is \(n = (\frac{1.96\sqrt{\sigma}}{4})^2\). If n is a decimal number, it is rounded up to the next integer. \(\sigma\) is the standard deviation of the population.

Answer:

this shape is a pentagon. this is a regular shape because all the sides are even and all the angles on the inside are also even.

Step-by-step explanation:

pls mark brainliest!

This is a classic riddle.3 quarters4 dimes0 nickels4 pennies If you have 4 quarters, you have change for 1 dollar.If you have 5 dimes, you have change for 2 quarters.If you have any nickels, 1 of those could combine with 2 dimes to have change for a quarter.If you have 5 pennies, you have enough change for 1 nickel. 3 * .25 + 4 * .10 + 4* .01 = x.75 + .40 + .04 = x1.19 = x

The measure of angle 1 in the given figure is 56 degrees.

From the image of the angle:

Measure of angle ABD = 62 degrees

Measure of angle 2 = 6 degrees

Measure of angle 1 = ?

From the diagram, angle 1 and angle 2 makes up angle ABD.

To solve for the missing angle ( angle 1 ), sum up both angle 1 and 2 and equate to angle ABD.

Hence:

Angle 1 + Angle 2 = Angle ABD

Plug in the values and simplify:

m∠1 + 6 = 62

Subtract 6 from both sides

m∠1 + 6 - 6 = 62 - 6

m∠1 = 62 - 6

m∠1 = 56 degrees

Therefore, angle 1 measures 56 degrees.

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After solving the equation, the value of y obtained is equal to 10°.

An angle results from the intersection of two lines at a point. The term "angle" describes the width of the "gap" that exists between these two rays. It's represented by the symbol ∠.

Angles are most frequently measured in degrees and radians, a measurement of roundness or rotation. Angles are a part of everyday existence.

As per the information obtained from the given figure,

Angle, C = 4y

Angle, E = 180 - 116 = 64 and,

Angle, D = 7y + 6

As we know, the sum of the angles of a triangle is 180°.

Then,

4y + 64 + 7y + 6 = 180

11y = 180 - 70

11y = 110

y = 110/11

y = 10°

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