While shopping at Target, Cathy sees a tank top that she loves for only $4.75. She decides to buy one in blue, red, and white. She pays the cashier with a $20.00 bill. How much change will Cathy get back from the cashier? (don’t factor in sales tax) *

The measures of the angles are: 64°  and 26°.

Recall: Two angles are complement of each other if they add up to the sum of 90° .

Thus,

Let \(x\) represent the first angle

The second angle = \((x-38)^{o}\)

Therefore:

\(x + (x - 38) = 90\)

Solve for x

\(x + x - 38 = 90\\2x - 38 = 90\\2x - 38 + 38 = 90 + 38\\2x = 128\\x = 64\)

The first angle, x, is 64°

The second angle = \(x - 38\)

Plug in the value of x

\(= 64 - 38\\= 26\)

Therefore, the measures of the two angles are 64°  and 26°

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Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

The elevation of the hole after placing the bush in the hole is 17/8 feet

Given: Davis digs a hole at a rate of 3/4 feet every 10 minutes

After digging for 40 minutes, Davis places a bush in the hole that fills exactly 7/8 feet of the hole

This involves subtraction and multiplication of fractions

Since the rate of digging = 3/4 feet every 10 minutes

Thus, after digging for 40 minutes, the depth will be:

3/4 × 4 = 3 feet

If Davis places a bush in the hole that fills exactly 7/8 feet of the hole, the remaining depth or elevation will be:

3 feet - 7/8 feet = 17/8 feet

Therefore,  after placing the bush in the hole, the elevation of the hole is 17/8 feet

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Histograms can be used to observe where the data tends to cluster.

What is a histogram?

A histogram is a visual depiction of data points arranged into ranges that the user has chosen. The histogram, which resembles a bar graph in appearance, groups numerous data points into comprehensible ranges or bins in order to compress a data series into an easily understood visual.

Histogram is used when data is in numbers and data tends to cluster. It is used to examine the data distribution's form. It is even used to evaluate whether the output differs when two or more processes are involved.

Hence, histograms can be used to observe where the data tends to cluster.

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Answer:

Yes its a function....good job!!!

Step-by-step explanation:

Answer:

centre = (- 6, - 1 ) , radius = 5

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

Given

x² + y² + 12x + 2y + 12= 0

Collect the x- terms and the y- terms together and subtract 12 from both sides

x² + 12x + y² + 2y = - 12

Using the method of completing the square

add ( half the coefficient of the x / y coefficients )² to both sides

x² + 2(6)x + 36 + y² + 2(1)y + 1 = - 12 + 36 + 1

(x + 6)² + (y + 1)² = 25 ← in standard form

with (h, k ) = - 6, - 1 ) as centre and r = \(\sqrt{25}\) = 5

Answer:

⚪ 3x - 9 + 2x²

Step-by-step explanation:

It is a quadratic equation.

\(.\)

The area of the plate covered by the napkin is (C) \(56cm^{2}\).

What is an area of a triangle?

To find the area of the plate covered by the napkin:

Given :

The following steps can be used in order to determine the area of the plate covered by the napkin:

Step 1 - The formula of the perimeter of a triangle is given below:

P = a + b + c   --- (1)

where a, b, and c are the length of the sides of the triangle.

Step 2 - According to the given data, the triangle is isosceles.

Therefore, the two sides are similar and the length of the base is 8 cm.

Step 3 - Now, substitute the values of the known terms in the above formula.

38 = 2L + 8

38 - 8 = 2L

L = 15 cm

Step 4 - The area of the plate covered by the napkin is given below:

\(A=\frac{1}{2} * 15 * 15 *Sin30\)

Step 5 - Simplify the above expression.

\(A=56.25cm^{2}\)

Rounding off to the nearest whole number, which is \(56cm^{2}\).

Therefore, the area of the plate covered by the napkin is (C) \(56cm^{2}\).

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The question you are looking for is here:

A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate, as shown. The napkin has a perimeter of 38 centimeters. To the nearest square centimeter, how many square centimeters of the plate is covered by the napkin?

(A) 16 square centimeters

(B) 30 square centimeters

(C) 56 square centimeters

(D) 60 square centimeters

Answer:

90

Step-by-step explanation:

all angels equal 180 so add the two you have then subtract 180 with the answer you got

Answer:

A,B,D

Step-by-step explanation:

Lebrone Jahames

Using limits, it is found that the infinite sequence converges, as the limit does not go to infinity.

Suppose an infinity sequence defined by:

\(\sum_{k = 0}^{\infty} f(k)\)

Then we have to calculate the following limit:

\(\lim_{k \rightarrow \infty} f(k)\)

If the limit goes to infinity, the sequence diverges, otherwise it converges.

In this problem, the function that defines the sequence is:

\(f(k) = \frac{k^3}{k^4 + 10}\)

Hence the limit is:

\(\lim_{k \rightarrow \infty} f(k) = \lim_{k \rightarrow \infty} \frac{k^3}{k^4 + 10} = \lim_{k \rightarrow \infty} \frac{k^3}{k^4} = \lim_{k \rightarrow \infty} \frac{1}{k} = \frac{1}{\infty} = 0\)

Hence, the infinite sequence converges, as the limit does not go to infinity.

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The series diverges by the comparison test.

We have for large enough \(k\),

\(\displaystyle \frac{k^3}{k^4+10} \approx \frac{k^3}{k^4} = \frac1k\)

so that

\(\displaystyle \sum_{k=0}^\infty \frac{k^3}{k^4+10} = \frac1{10} + \sum_{k=1}^\infty \frac{k^3}{k^4+10} \approx \frac1{10} + \sum_{k=1}^\infty \frac1k\)

and the latter sum is the divergent harmonic series.

Answer:

15.733in^2

Step-by-step explanation:

For this triangle it would be area=0.5 * b * h * sin(y)

(y) being the angle

(b) being base

(h) being height

Hope this helps and I am pretty sure this is right.

Answer:

is 24

Step-by-step explanation:

because is multiply for 22

Answer:

No

Step-by-step explanation:

11-(-5)=16

-5+(11)=6

Answer:

b.

Step-by-step explanation:

We have been given a number 8¼. We are asked to find the opposite of the opposite of our given expression.

Since our given number in positive, so opposite of our given number will be:

–8¼

The opposite of new number will be:

–(–8¼)

Therefore, the expression –(–8¼) represents the opposite of the opposite of 8¼ and option 'b' is the correct

The height of the building from the ground is 83.33 m.

Let h be the height of the building, d be the distance between point A and the building, and d' be the distance between point B and the building.

From the problem, we know that:

We can use trigonometry to find the height of the building:

h / d = tan 58°

h = d * tan 58°

Also,

h / d' = tan 27°

h = d' * tan 27°

Since h is the same for both equations, we can set them equal to each other and solve for d:

d * tan 58° = d' * tan 27°

d = d' * tan 27° / tan 58°

We also know that point B is 80 m due West of point A, so we can use the Pythagorean theorem to find the value of d':

d' = √(80² + h²)

Now, we can substitute that into the equation for d and solve for h:

d = d' * tan 27° / tan 58°

h/tan 58° = √(80² + h²) * tan 27° / tan 58°

h=√(80² + h²)*tan 27°

h²cot²27= 80²+h²

1.96h²= 80²+h²

0.96h²=80²

h²= 6944.44

h= 83.33

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The likelihood that a randomly selected bag of cement weighs more than 50 is approximately 93.32%

When dealing with normally distributed data, we use the mean and standard deviation to determine the likelihood of certain events occurring. In this case, the mean weight of bags of cement is 53 with a standard deviation of 2.

To find the likelihood that a randomly selected bag has a weight greater than 50, we need to calculate the z-score for 50. The z-score tells us how many standard deviations away a particular value is from the mean.

z = (X - μ) / σ

where X is the value we're interested in (50), μ is the mean (53), and σ is the standard deviation (2).

z = (50 - 53) / 2 = -1.5

A z-score of -1.5 means that a weight of 50 is 1.5 standard deviations below the mean. To find the likelihood of a bag weighing more than 50, we can use a z-table or a calculator to find the area to the right of this z-score.

Looking up a z-score of -1.5, we find that the area to the left is approximately 0.0668, which means the area to the right (the likelihood of a bag weighing more than 50) is:

1 - 0.0668 = 0.9332

Thus, the likelihood that a randomly selected bag of cement weighs more than 50 is approximately 93.32%.

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T test is used to compute the confidence interval, when the mean and standard deviation is given.

What is Standard Deviation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be very close to the set mean. The lower case Greek letter (sigma), again for population standard deviation, or even the Latin letter s, again for sample standard deviation, are most frequently used in mathematical texts and equations to represent standard deviation. Standard deviation may be abbreviated as SD. A random variable, specimen, statistical population, data set, as well as probability distribution's standard deviation is equal to the square root of its variance. When the number in a sample, sample mean and sample standard deviation is given, the test statistic that should be used when computing a confidence interval is t test

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The value of cos(2x) is -7/25 when csc(x) = 4/3 (in Quadrant 1).

To find cos(2x), we can use the double angle identity for cosine: cos(2x) = 2cos ²(x) - 1.

Given that csc(x) = 4/3 in Quadrant 1, we can determine the value of sin(x) using the reciprocal relationship between sine and cosecant: sin(x) = 1/csc(x) = 3/4.

Using the Pythagorean identity, we can find the value of cos(x): cos(x) = √(1 - sin ²(x)) = √(1 - (3/4) ²) = √(1 - 9/16) = √(7/16) = √7/4.

Now, substituting this value into the double angle identity, we get: cos(2x) = 2(√7/4) ² - 1 = 2(7/16) - 1 = 7/8 - 1 = 7/8 - 8/8 = -1/8.

Simplifying further, we have cos(2x) = -1/8 = -7/56 = -7/25 (approximated to 4 decimal places).

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Answer:i think its 115 degres

Step-by-step explanation:

Answer:

( B.) 6, 1, -2 , -4

Step-by-step explanation:

A coefficient is a number multiplied by a variable. So, in this case let's take a look at the problem.

-2+6y+m-2y+8-4m

Now we have to find the numbers that have a variable next to it

which are 6,m,-2, and -4

(If you are wondering that why m is a coefficient its because it is also known as 1m)

Final answer = 6, 1, -2 , -4

Hope this helps!

The operation that Amjed should perform to determine the relative frequency of a person over 30 years old who prefers to ride a mountain bike is given as follows:

2) Divide 25 by 462.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of people is given as follows:

58 + 164 + 215 + 25 = 462.

Out of these people, 25 prefer mountain bike, hence the relative frequency is given as follows:

25/462.

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The new mean of the data-set, with the observation 2 removed, is given as follows:

12.67 attempts.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.

Removing the observation 2, the data-set is given as follows:

11, 11, 11, 12, 13, 13, 14, 14, 15.

The sum of all these observations is given as follows:

3 x 11 + 12 + 2 x 13 + 2 x 14 + 15 = 114.

There are nine observations, hence the mean of these observations is given as follows:

114/9 = 12.67.

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By the principle of mathematical induction, the formula holds true for all positive integers n. Hence, the statement is proved.

To prove the statement using induction, we will first establish the base case and then demonstrate the inductive step.

Base Case:

Let n = 1. In this case, the sum is:

1(1)(3)/(3) = 1

The sum for n = 1 satisfies the given formula.

Inductive Step:

Assume that the formula holds true for an arbitrary positive integer k, i.e.,

1 + 1(3)(5)/(3) + 1(5)(7)/(5) + ... + 1(2k-1)(2k+1)/(2k-1) = (2k+1)

Now, we need to show that the formula also holds for k + 1, i.e.,

1 + 1(3)(5)/(3) + 1(5)(7)/(5) + ... + 1(2k-1)(2k+1)/(2k-1) + 1(2(k+1)-1)(2(k+1)+1)/(2(k+1)-1) = 2(k+1)+1

We start with the left-hand side (LHS) of the equation:

LHS = 1 + 1(3)(5)/(3) + 1(5)(7)/(5) + ... + 1(2k-1)(2k+1)/(2k-1) + 1(2(k+1)-1)(2(k+1)+1)/(2(k+1)-1)

Next, we simplify the last term of the LHS:

1(2(k+1)-1)(2(k+1)+1)/(2(k+1)-1)

= (2(k+1)-1)(2(k+1)+1)

= (2k+3)(2k+1)

Now, we substitute the assumption into the LHS:

LHS = (2k+1) + (2k+1)(2k+3)

= (2k+1)(1 + (2k+3))

= (2k+1)(2k+4)

= (2k+1)(2(k+2))

= 2(k+1)(k+2)

= \(2(k+1)^2 + 2(k+1)\)

We can rewrite \(2(k+1)^2 + 2(k+1) as 2(k+1)(k+1) + 2(k+1) = 2(k+1)((k+1)+1)\).

Now, we can see that the LHS is equal to the expression (2(k+1)+1). Hence, the formula holds true for k + 1 as well.

By the principle of mathematical induction, the formula holds true for all positive integers n.

Therefore the statement is proved.

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Answer:

154

Step-by-step explanation:

154/22=7

Answer:

(4 , - 35)

Step-by-step explanation:

X²-8x-19 =(x-4)² -35

y = a (x-h)² + k    a=1   , (h , k) -> (4 , - 35)

Answer:

Yes i do the answer is C

Step-by-step explanation:

Have a good day:))))

The change in kinetic energy of a body can be calculated by multiplying the force applied to the body by the distance it moves. In this case, a body of mass 20 kg is subjected to a force of 40 N for 5 seconds.

The change in kinetic energy (ΔKE) can be calculated using the formula ΔKE = F * d, where F is the force applied and d is the distance covered by the body. However, in this case, we are only given the force and the time (5 seconds), but not the distance.

To calculate the change in kinetic energy, we need to consider the relationship between force, mass, acceleration, and distance covered. According to Newton's second law of motion (F = m * a), we can determine the acceleration (a) experienced by the body by dividing the force by the mass: a = F / m.

Once we have the acceleration, we can use the kinematic equation v = u + at, where v is the final velocity, u is the initial velocity (which is zero since the body is initially at rest), a is the acceleration, and t is the time. Solving for v, we get v = a * t.

Since the body starts from rest, the initial kinetic energy is zero. The final kinetic energy can be calculated using the formula KE = (1/2) * m * \(v^2\), where m is the mass and v is the final velocity obtained from the previous step.

Therefore, to find the change in kinetic energy, we subtract the initial kinetic energy (zero) from the final kinetic energy calculated.

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Answer:

B-The flare signal was set off at a height of 3 feet.