William says that 15 years from now, his age will be 3 times his age 5 years ago. If x represents William’s present age, complete the following sentences.

a)15 years
b)18 years
c)x − 15 = 3(x + 5)
d)x + 15 = 3(x − 5)

The inequality shows that Nicholas will swim more than Alex on the 21st day of July.

In June, Alex swam 30 miles and Nicholas swam 18 miles. Therefore, Alex swam an average of 30/30 = 1 mile per day and Nicholas swam an average of 18/30 = 0.6 miles per day.

Starting in July, Alex will swim one mile per day. If we assume that Nicholas also starts on July 1st, he will swim 2-0.6 = 1.4 miles more per day than Alex.

1 + 1.4x > 30

where x is the number of days since July 1st.

Simplifying this equation, we get:

1.4x > 29

x > 20.7

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Mr. Lin says that XYZ is not a dilations of STU, he is correct

Dilations:-

                A sort of transformation known as a dilatation, enlarges or shrinks a figure (referred to as the preimage) to produce a new figure (called the image). How much larger or smaller the dilation image will be in comparison to the preimage depends on the scale factor, k. The value of k will always be greater than zero.

     Scale Factor is defined as the ratio of the size of the new image to the size of the old image

                k= size of new image/size of old image

Here in given question/figure,

         for  ΔSTU  

             ST=8 in.

             TU=12 in.

              US=15 in.

and   for ΔXYZ

            XY=2 in.

            YZ=3 in.

            ZX=4 in.

Scale factor for for side ST to XY is  

                       k= 2/8=0.25

Scale factor for for side TU to YZ is

                      k=3/12=0.25

Scale factor for for side US to ZX is

                     k=4/15=0.26

We can see all the scale factors are not equal.

Hence, we can say for the figure are not dilations of each other.

   Thus, Mr. Lin says that XYZ is not a dilations of STU, he is correct

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The two positive numbers are 39 and 91 in the ratio 3:7

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Let x and y represent the two positive numbers. x represent the smaller while y is the larger

Two positive numbers are in the ratio 3:7, hence:

(3/10)(x + y) = x

3x + 3y = 10x

7x - 3y = 0   (1)

Their difference is 52, hence:

y - x = 52   (2)

From both equations:

x = 39, y = 91

The two numbers are 39 and 91

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The coefficient of the squared term in the parabola's equation is 1/25.

In this exercise, you are required to determine the factored form of the given quadratic function that passes through the points (2, -4) and (-3, -3).

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided above, we can determine the value of a as follows:

f(x) = a(x - h)² + k

-3 = a(-3 - 2)² - 4

-3 = 25a - 4

1 = 25a

a = 1/25

Therefore, the required quadratic function is given by:

f(x) = a(x - h)² + k

f(x) = y = 1/25(x - 2)² - 4

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Answer:

D. No. She multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

Step-by-step explanation:

A. Yes. She solved the problem correctly.

B. No. She multiplied the dividend by the divisor instead of finding the reciprocal.

C. No. She multiplied the denominators instead of finding a common denominator.

D. No. She multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

Her workings

7 ÷ 2/ 5

=1/ 7 × 2/ 5

= 2/35

Dividend=7

Divisor=2/5

The correct working

7 ÷ 2/ 5

=7 × 5/2

=35/2

Answer:

D

Step-by-step explanation:

I got an 100% on the quiz I took with this question :)

Hope I could help good luck on passing!!

A scientific calculator is typically used for pre-calculus.

This type of calculator is designed to handle more advanced mathematical functions, such as trigonometry, logarithms, and exponents, which are commonly used in pre-calculus.

It is important to have a scientific calculator for pre-calculus because it allows you to easily solve more complex equations and perform calculations quickly and accurately.

Additionally, many scientific calculators have graphing capabilities, which can be useful for visualizing equations and understanding how they behave. Overall, a scientific calculator is an essential tool for pre-calculus and can help you succeed in the course.

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The solution to the given system of linear equations is x = 4, y = 20

From the question, we are to determine solution to the given system of equations

The given system of equations is

x+y=6x=y+4

Thus, we can write that

x + y = 6x ----------- (1)

and

6x = y + 4 ------------(2)

Solve the two equations simultaneously

From equation (1)

x + y = 6x

y = 6x - x

y = 5x --------- (3)

Substitute into equation (2)

6x = y + 4

6x = 5x + 4

6x - 5x = 4

x = 4

Substitute the value of x into equation (3)

y = 5x

y = 5(4)

y = 20

Hence, the solution to the given system of linear equations is x = 4, y = 20

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The correct answer is k+3 ke-2.

To determine which formula is not equivalent to the other two, we can compare each formula step-by-step. Let's analyze each formula:

1. (-1k-3 k +3 k+ 4 ks4
2. k+3 ke-2
3. k-3 ks4

Starting with formula 1, we can see that it consists of three terms: -1k-3, k+3, and k+4ks4. Each term is separated by a space.

Moving on to formula 2, we have k+3ke-2. This formula also consists of three terms: k+3, k, and e-2. In this case, we have a variable (k) combined with two different exponents (3 and -2).

Finally, formula 3 is k-3ks4. It consists of two terms: k-3 and ks4. Again, each term is separated by a space.

Comparing the three formulas, we can see that formula 1 has three terms, while formulas 2 and 3 have two terms each. Additionally, formula 1 includes the term k+4ks4, which is not present in formulas 2 and 3.

Therefore, the formula that is not equivalent to the other two is k+3 ke-2.

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The horizontal distance from the tower to the fire is 7 feet

The term "angle of depression" describes the angle created by a horizontal line and the line of sight from the observer's eye to a location below their horizontal line of sight. It is often calculated by descending from the horizontal line.

The angle of depression is a term that is frequently used in discussions of observations or measurements involving objects that are below the observer's location in geometry and trigonometry.

We know that;

Tan 3 = x/140

x = 140 Tan 3

x = 7 feet

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Answer:

13

Step-by-step explanation:

70 - 5 = 65

125 - 8 = 117

Find the Greatest Common Divisor of 65 & 117

65 = 5 * 13

117 = 3 * 3 * 13

GCD = 13

13 is the largest number that divides 70 & 125 and leaves remainders 5 and 8 respectively

Answer:

\(3.5 - 2 \times 100 \div 2\)

Answer:

The percentage increase in the puppy's weight is 75%.

Step-by-step explanation:

We can find the percentage increase using the following formula:

\(\boxed{\% \space\ \mathrm {increase = \frac{final \space\ - \space\ initial}{initial} \times 100}}\).

In this case,

• initial = 2 kg

• final = 3.5 kg

Substituting these values into the formula:

\({\% \space\ \mathrm {increase = \frac{3.5 \space\ - \space\ 2}{2} \times 100}}\)

                ⇒ \(\frac{1.5}{2} \times 100\)

                ⇒ \(0.75 \times 100\)

                ⇒ 75%

Answer:

im sry but i have no idea

Step-by-step explanation:

It appears that you have created a relative-frequency distribution graph for some data (possibly related to investment returns) and would like to use a normal density function to model future returns. The most important assumption to consider in this context is the assumption of normality.

The normality assumption states that the underlying data follows a normal distribution, also known as the Gaussian distribution or bell curve. This distribution is characterized by its symmetric bell shape and is defined by its mean (average) and standard deviation (a measure of variability). In a normal distribution, about 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

When using the normal density function to model future returns, it is crucial to assume that the data exhibits normality. This means that the relative frequencies of the returns in the dataset follow the pattern expected from a normal distribution. If the data significantly deviates from normality, the predictions made using the normal density function might not be accurate and could lead to poor decision-making in future investment scenarios.

In summary, the most important assumption to consider when using a normal density function to model future returns based on a relative-frequency distribution graph is that the data follows a normal distribution. This assumption allows for accurate predictions and better decision-making in investment planning.

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2. Clem Shirestock is running for his life from the cultists whose ritual he's just disrupted on the fourth floor of an old building in the slums of Altdorf. He can't make his way down the stairs, and finds himself on a

balcony, looking at a three story building's flat roof just across the alley. While Clem knows, from his

surveillance of the area, that the alley is about 4 yards across, and estimates that the roof of the building (that he hopes he may be able to jump to) is at about a 25-degree angle down from the balcony. How far is it to the roof if he makes the jump? (To the nearest tenth of a yard.)

________________________________________________________

Problem outline

_______________________________________

tan 65 = b/a

b= tan 65 / a

b= tan 65 / 4 yards

b= 2.14/4

b= 0.536

___________________________

The roof is about 0.5 yards

First, let's list all the possible arrangements of the digits 2, 4, and 6 with a decimal point between two digits: - 2.4.6
- 2.6.4
- 4.2.6
- 4.6.2
- 6.2.4
- 6.4.2

Now, we need to find the sum of every number less than 4.4 than grogg writes. This means we need to add up all the numbers that are less than 4.4 and are also less than each of the six numbers on our list.

Let's start with the first number on our list, 2.4.6. The numbers that are less than 4.4 and less than 2.4.6 are:

- 2.4
- 2.6

So we add those two numbers together:  2.4 + 2.6 = 5, That's the sum for the first number on our list. Now we can repeat this process for each of the other five numbers on our list, and add up all the sums at the end. For 2.6.4, the numbers less than 4.4 and less than 2.6.4 are: - 2.6 .

So the sum for 2.6.4 is:  2.6, For 4.2.6, the numbers less than 4.4 and less than 4.2.6 are:
- 4.2
- 4.6, So the sum for 4.2.6 is: 4.2 + 4.6 = 8.8, For 4.6.2, the numbers less than 4.4 and less than 4.6.2 are:
- 4.2
- 4.6

So the sum for 4.6.2 is:
4.2 + 4.6 = 8.8

For 6.2.4, the numbers less than 4.4 and less than 6.2.4 are:

- None

There are no numbers less than 4.4 and less than 6.2.4, so the sum for 6.2.4 is 0.
Finally, for 6.4.2, the numbers less than 4.4 and less than 6.4.2 are:
- None

Again, there are no numbers less than 4.4 and less than 6.4.2, so the sum for 6.4.2 is 0.
Now we can add up all the sums:  5 + 2.6 + 8.8 + 8.8 + 0 + 0 = 25.2

So the sum of every number less than 4.4 than grogg writes is 25.2.

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The phase constant for the harmonic oscillator with the velocity function v(t), if the position function has the form x(t) = x_m cos(ωt + φ)  is: -0.927 rad

We are told that the vertical scale is set as: v_s = 4.0 cm/s

Using the formula of velocity, we can find the phase constant for the harmonic oscillator from the position function of form,

x(t) = x_m cos(ωt + φ)

The velocity of a body in motion is expressed as:

v = dx/dt  -----(i)

Equation of displacement of the motion:

x(t) = x_m cos(ωt + φ)    -----(ii)

Differentiating equation (ii), we get:

v = -v_m sin (ωt + φ)    -----(iii)

Using the values of t = 0 s, v_m = 5 cm/s, v = 4 cm/s in equation (iii), we get:

4 = -5 sin  (ω(0) + φ)  

φ = sin⁻¹(4/5)

φ = -0.927 rad

Therefore, the phase constant for the harmonic oscillator with the velocity function v(t), if the position function has the form x(t) = x_m cos(ωt + φ)  is -0.927 rad

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Complete question is:

What is the phase constant for the harmonic oscillator with the position function x(t) given in the plot if the position function has the form x = x_m cos(ωt + φ). The vertical axis scale is set as v_s = 4.0 cm/s

The correct option is (B) the isometric transformation was possible due to the vertices' uniform 2 units to the right and 2 units downward displacement.

The process of turning a graph into a new graph using rotation, reflection, translation, and dilation is known as transformation.

An object is said to be rotated when it is turned by a specific amount in either the clockwise or counterclockwise directions on an x-y plane.

Reflection turns an object into a mirror image that is identical in terms of size and shape with just the coordinates altered.

Moving an item up, down, left, or right on a coordinate axis is known as translation.

Dilation is the process of modifying an object's size; the original object is either compressed or enlarged by a specific scale factor.

So, the coordinates for the object ABC in the image are A (-2, 5), B (-5, 3), C(1, 3), and.

The picture's coordinates are A'(0,3), B'(-5,-3), and C' (3, -5).

The coordinates have undergone a translational transformation.

The vertices all shifted 2 units to the right and 2 units down, allowing an isometric transformation to be applied.

Therefore, the correct option is (B) the isometric transformation was possible due to the vertices' uniform 2 units to the right and 2 units downward displacement.

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Complete question:

Which describes the transformation that could have been applied to triangle ABC?

a. A dilation could have been applied because all of the vertices decreased by 2 units.

b. An isometric transformation could have been applied because all of the vertices moved 2 units right and 2 units down.

c. A dilation could have been applied because all of the vertices increased 2 units.

d. An isometric transformation could have been applied because all of the vertices moved 2 units left and 2 units up.

The function r(x) is an example of a Pade approximation to f(x). it is not always possible to find such an approximation r(x). However,

It is not always possible to find an approximation r(x). However, the function r(x) is an example of a Pade approximation to f(x).

What is Pade approximation A Pade approximation is a technique for approximating a function using a ratio of two polynomials. This approximation is used to approximate functions that may be difficult to compute or solve exactly.

Pade approximations are often used in numerical analysis, scientific computing, and engineering to obtain accurate solutions to problems that are too complicated or expensive to solve exactly.How to find an approximation r(x) To find an approximation r(x), we need to find a ratio of two polynomials that approximates f(x).

The Pade approximation r(x) is given by the ratio of two polynomials: P(x) and Q(x). The P(x) and Q(x) are usually chosen to be of the same degree to minimize the error between the approximation and the exact value of f(x).Therefore, it is not always possible to find such an approximation r(x). However, the function r(x) is an example of a Pade approximation to f(x).

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The interpretation of the 95% confidence interval is that we are 95% confident that the true mean yield of chemical processes using catalyst A falls within the range of 90.16 to 94.36.

To calculate the 95% confidence interval for the true mean yield of chemical processes that use catalyst A, we can use the formula:

Confidence interval = sample mean ± (critical value) * (standard deviation / √(sample size))

Given the information:

Sample mean (x') = 92.26

Standard deviation (s) = 2.39

Sample size (n) = 8

First, we need to find the critical value corresponding to a 95% confidence level. Since the sample size is small (n = 8), we use a t-distribution. With 7 degrees of freedom (n-1), the critical value for a 95% confidence level is approximately 2.365.

Next, we can calculate the confidence interval:

Confidence interval = 92.26 ± (2.365 * (2.39 / sqrt(8)))

Calculating this expression, we get the confidence interval as (90.16, 94.36).

This means that if we were to repeat the sampling process and construct multiple confidence intervals, approximately 95% of those intervals would contain the true mean yield.

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The value of x for the length A'E' of the similar shape A'B'C'D'E' is equal to 6⅔.

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other.

The side A'E' corresponds to the side A'E' and also E'D' corresponds to the side ED so;

(7). A'E'/AE = E'D'/ED

x/10 = 6/9

x = (10 × 6)/9 {cross multiplication}

x = 20/3

x = 6⅔

Therefore, the value of x for the length A'E' of the similar shape A'B'C'D'E' is equal to 6⅔

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Answer:

100

Step-by-step explanation:

1_2_3_4_5_6_7_8_9_0

Answer:

-16

Step-by-step explanation:

-12-128/2/4^2=

-12-64/4^2=

-12-64/16=

-12-4=

-16

Answer:

-16.

Step-by-step explanation:

Using order of operations (PEMDAS):

-12 - 128 ÷ 2 ÷ 4^2    First do the exponential term

-12 − 128 ÷ 2 ÷ 16   Do the leftmost  division first:

= -12 - 64  ÷ 16       Now the division

= -12 - 4

= -16.

So answer is true For deductive arguments, you answer true to the question “Do the premises provide enough logical support for the conclusion

A valid argument is a deductive argument that succeeds in providing decisive logical support.

A valid argument is thus a deductive argument an argument that attempts to establish conclusive support for its conclusion  that succeeds.

An invalid argument is a deductive argument that fails in providing conclusive support.

For deductive arguments, you answer “yes” to the question “Do the premises provide enough logical support for the conclusion?” if the argument is valid, and you answer “no” if otherwise.

So answer is true For deductive arguments, you answer true to the question “Do the premises provide enough logical support for the conclusion

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Answer:

8y - 15

Step-by-step explanation:

-y - 3(-3y+5)

-y + 9y - 15

8y - 15

Answer:

8y - 15 is the equivalent to the expression -y - 3(-3y + 5).

Step-by-step explanation:

= -y - 3(-3y + 5)

= -y + 9y - 15

= 8y - 15

The actual price is 13.6% lower than the expected price.

CPI or Consumer Price Index is a measure of determining retail inflation in an economy, based on price variations in a fixed basket of goods and services, over overtime periods.

Let's suppose the expected price is x.

The percent relation of the actual price of a winter hat to the expected price is given by;

CPI = ( expected price ) : ( price in 1983 ) × 100

219  =  ( x  : 12.95 ) × 100

Divide both sides by 100.

x : 12.95 = 2.19

x =2.19 × 12.95

x = $28.36 ( expected price )

p = ( 24.50 × 100 ) / 28.36

p= 2450/28.36

p = 86.4 %

100 % - 86.4 % = 13.6 %

Hence, the actual price is 13.6% lower than the expected price.

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Answer:A boo

Step-by-step explanation: trust me :) ✨