Nancy borrowed $150 from her parents to buy a video game system. She has agreed to pay them back $25 each week Which equation represents the amount of money

Nancy still owes her parents, P. after w weeks?

Answer:

Solution,

from the figure,height of ∆ DBC=36-h

Now,in two similar triangles, ratio of corresponding sides are equal to ratio of their heights.

Since, ∆DBC~∆EBA

\( \frac{36 - h}{h} = \frac{dc}{ae} \\ or \: \frac{36 - h}{h} = \frac{10}{20} \\ or \: 20(36 - h) = 10 \times h(cross \: multiplication) \\ or \: 720 - 20h = 10h \\ or \: - 20h - 10h = - 720 \\ or \: - 30h = - 720 \\ or \: h = \frac{ - 720}{ - 30} \\ h = 24 \: cm\)

Height of ABE =24 cm

hope this helps...

Good luck on your assignment...

Answer:

24cm

Step-by-step explanation:

\( - 13 = \frac{w}{9} - 6 \\ - 13 + 6 = \frac{w}{9} \\ - 7 = \frac{w}{9} \\ w = - 63\)

so only -63 is the solution, the rest three are NOT solution for this equation.

1. first we are going to solve from the internal to the external, we will start step by step first the numerator we start with the power then we add the internal parenthesis then we subtract and finally we will solve the denominator that is the bottom part.

the negative adds the negative of 6 and remains positive,and since 25 is a prime and 16 is an even number, so the answer cannot be simplified.

The greatest common divisor of 5! and 7! is 840.

To find the greatest common divisor (GCD) of 5! and 7!, we need to calculate the prime factorization of both numbers.

First, let's calculate the prime factorization of 5!:

5! = 5 * 4 * 3 * 2 * 1 = 120.

The prime factorization of 120 is 2^3 * 3 * 5.

Now, let's calculate the prime factorization of 7!:

7! = 7 * 6 * 5! = 7 * 6 * 120 = 5040.

The prime factorization of 5040 is 2^4 * 3^2 * 5 * 7.

To find the GCD of 5! and 7!, we need to find the common factors in their prime factorizations. We take the smallest exponent for each prime factor that appears in both factorizations.

From the prime factorizations above, we can see that the common factors are 2^3, 3, 5, and 7. Multiplying these factors together gives us:

GCD(5!, 7!) = 2^3 * 3 * 5 * 7 = 8 * 3 * 5 * 7 = 840.

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Answer:

11 minutes will it take him to type 385 words.

Step-by-step explanation:

i hope this help

Answer: 15 minutes

Step-by-step explanation:

You graph >7 with an open dot to the right.

The inequalities ≤ and ≥ would have a closed dot on the number line.

a > 3 is matched to the statement; "you must be older than 13 to play in the basketball league".

s < 3.5 is matched to the statement; "To use one stamp, your domestic letter must be under 3.5 ounces".

t ≥ 48 is matched to the statement; "You must be at least 48 inches tall to ride on the rollercoaster".

Inequality signs are mathematical symbols used to indicate that one quantity is greater than, less than, or equal to another quantity. These inequality signs includes:

These symbols are used in mathematical expressions and equations to compare values and express relationships between them.

Therefore, with a good understanding of inequality signs we conclude that:

On a graph, > 7 is with an open dot to the right.

Only the inequalities ≤ and ≥ would have a closed dot on the number line.

a > 3 is matched to the statement; "you must be older than 13 to play in the basketball league".

s < 3.5 is matched to the statement; "To use one stamp, your domestic letter must be under 3.5 ounces".

t ≥ 48 is matched to the statement; "You must be at least 48 inches tall to ride on the rollercoaster".

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Answer:

your answer is 91 over 5

Step-by-step explanation:

Answer:

its 2 with a power of 3 over ten.

Step-by-step explanation:

I got it wrong and just clicked show correct answer.

Answer:

42 units

Step-by-step explanation:

Area of a trapezoid is always 1/2(b1+b2)*h

so here base 1 is 4 units, and base 2 is 10 units. When we add these we get 14, divided by 2 which is 7, and multiplied by height of 6, which is 42

The result of the product for the following pairs of number is irrational for 1. Option d √2(4). 2. Option a. 3. Option d. 4. Option b.

A real number that cannot be stated as a ratio of integers is said to be irrational; an example of this is the number √2. Any irrational number, such as p/q, where p and q are integers, q≠0, cannot be expressed as a ratio. Once more, an irrational number's decimal expansion is neither ending nor recurrent.

1. The product of the numbers are:

a. √2 (√8) = √16 = 4

b. √49 (∛ 8) = 14

c. √3 (2/ √3) = 2

d. √2(4)

Option d is the correct answer.

Similarly, taking the product:

2. Option a is correct.

3. Option d is correct.

4. Option b is correct.

Hence, the result of the product for the following pairs of number is irrational for 1. Option d √2(4). 2. Option a. 3. Option d. 4. Option b.

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The solution of the expression is,

⇒ x = - 1 and x = 5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Solve the expression,

x² – 3x − 2 = x + 3

Now, We can simplify as;

x² – 3x − 2 = x + 3

x² – 3x − 2 - x - 3 = 0

x² - 4x - 5 = 0

x² - 5x + x - 5 = 0

x (x - 5) + 1(x - 5) = 0

(x + 1) (x - 5) = 0

x = - 1

x = 5

Thus, The solution of the expression is,

⇒ x = - 1 and x = 5

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The correct option A) There is a cluster, and as x decreases, y increases.

The table represents a set of data containing two variables, x and y. By analyzing the data, we can observe a cluster of values around x = 4 with corresponding y values in the range of 42-45. As we move towards smaller x values, there is a general trend of increasing y values. However, there are a few outliers. Based on these observations, statement A is the most accurate description of the data in the table. It is important to note that the accuracy of the statement is limited to the given data, and further analysis or additional data may reveal a different trend or pattern.

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Complete question:

The table below shows a set of data. Which statement about the table is true?

x: 1.6, 1.9, 2.3, 3.4, 3.8, 4.2, 4.3, 4.6, 4.8.

y: 39, 38, 42, 40, 41, 44, 42, 45, 44

Which statement about the table is true?

A) There is a cluster, and as x decreases, y increases.

B) There is a cluster, and as x increases, y increases.

C) There is not a cluster, and as x increases, y increases.

D) There is not a cluster, and as x decreases, y increases.

The probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 8/25 or 0.32 (rounded to the nearest millionth).

1. Calculate the total number of students on the Student Government Board by summing up the numbers in the table:

  Total Students = 2 + 2 + 2 + 4 + 0 + 3 + 4 + 2 = 19

2. Calculate the total number of graduate students on the Student Government Board:

  Total Graduate Students = 2 + 0 = 2

3. Calculate the total number of students living in on-campus housing:

  Total On-Campus Housing = 2 + 2 + 0 + 4 + 2 = 10

4. Calculate the probability of selecting a graduate student from the Student Government Board by dividing the total number of graduate students by the total number of students:

  Probability of Graduate Student = Total Graduate Students / Total Students = 2 / 19

5. Calculate the probability of selecting a student living in on-campus housing by dividing the total number of students in on-campus housing by the total number of students:

  Probability of On-Campus Housing = Total On-Campus Housing / Total Students = 10 / 19

6. Calculate the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing by summing up the probabilities from steps 4 and 5:

  Probability = Probability of Graduate Student + Probability of On-Campus Housing = 2 / 19 + 10 / 19

7. Simplify the fraction if necessary. In this case, the fraction cannot be simplified further, so the final probability is 2 / 19 + 10 / 19 = 12 / 19.

8. Convert the fraction to a decimal by dividing the numerator by the denominator: 12 / 19 ≈ 0.631578947, which rounds to 0.632 (rounded to the nearest thousandth).

9. Finally, express the probability as a fraction in lowest terms: 12 / 19 is already in lowest terms.

Therefore, the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 12/19 or approximately 0.632 (rounded to the nearest thousandth).

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The exponential function that represents this situation is f(x) = 42 * (0.85)ˣ

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

Inital growth, a = 42

Rate of decrease, r = 15%

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

The function of the situation is

f(x) = a * (1 - r)ˣ

Substitute the known values in the above equation, so, we have the following representation

f(x) = 42 * (1 - 15%)ˣ

So, we have

f(x) = 42 * (0.85)ˣ

Hence, the function is f(x) = 42 * (0.85)ˣ

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Question

Growth was worth $42 at tje beggining of the day. event every hour stock goes down by 15%. Write the exponential function that represents this situation.

Fοr Marquita, the best methοd wοuld be -Optiοn B: Cοmpare her percent cοrrect οn each test.

The term "percentage" in mathematics refers tο a value οr ratiο that can be expressed as a fractiοn οf 100. If a percentage οf a number needs tο be calculated, it shοuld first be divided by 100 and then multiplied by 100. A cent per hundred is what is meant by the preceding paragraph.

Marquita shοuld use Ptin (b), which cοmpares her percent cοrrect οn each test, tο cοmpare her perfοrmance οn each test.

This methοd will give her an idea οf hοw well she understοοd the material and hοw accurately she was able tο answer the questiοns οn each test.

Cοmparing her tοtal scοres οr the number οf questiοns she missed may nοt give her an accurate reflectiοn οf her perfοrmance, as sοme tests may have had mοre questiοns οr been wοrth mοre pοints than οthers.

Cοmparing her z-scοres wοuld require her tο have the mean and standard deviatiοn fοr each test, which may nοt be available.

Therefοre, cοmparing percent cοrrect wοuld be the mοst straightfοrward and useful methοd fοr Marquita tο cοmpare her perfοrmance οn each test.

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Answer:

Yes. There is enough evidence to support the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.

Step-by-step explanation:

We want to test the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.

To perform this test we have a sample of 500 students which have paid their balance in full each month. The sample mean is $825 and the estimated sample deviation is considered $200.

Then, the null and alternative hypothesis are:

\(H_0: \mu=905\\\\H_a:\mu< 905\)

The significance level is 0.05.

The sample has a size n=500.

The sample mean is M=825.

The estimated standard error of the mean is computed using the formula:

\(s_M=\dfrac{s}{\sqrt{n}}=\dfrac{200}{\sqrt{500}}=8.94\)

Then, we can calculate the t-statistic as:

\(t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{825-905}{8.94}=\dfrac{-80}{8.94}=-8.94\)

The degrees of freedom for this sample size are:

\(df=n-1=500-1=499\)

This test is a left-tailed test, with 499 degrees of freedom and t=-8.94, so the P-value for this test is calculated as (using a t-table):

\(\text{P-value}=P(t<-8.94)=0\)

As the P-value (0) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.

Answer:

200.96

Step-by-step explanation:

Answer:

x = 111

Step-by-step explanation:

180- 82 -29 is 69 and 180-69 is x which x is equal to 111

Answer:

111°

Step-by-step explanation:

By exterior angle theorem:

\(x = 82 \degree + 29 \degree \\ = 111 \degree\)

Answer:

yes

Step-by-step explanation:

Answer:

412 (pls add the unit cuz i dont learn yd thx)

Step-by-step explanation:

13*12/2*4 + 10*10

= 312 + 100

= 412

The total number of different signals consisting of flags is 216

Given data ,

The number of different signals consisting of 9 flags that can be made using 3 white flags, 3 red flags, and 3 blue flags can be calculated using combinatorial principles.

There are 3 choices for the top flag (white, red, or blue), 2 choices for the second flag (since we've already used one color for the top flag), and 1 choice for the third flag.

Similarly, there are 3 choices for the fourth flag, 2 choices for the fifth flag, and 1 choice for the sixth flag. Finally, there are 3 choices for the seventh flag, 2 choices for the eighth flag, and 1 choice for the ninth flag.

Using the multiplication principle, we can multiply the number of choices at each step to get the total number of different signals:

3 × 2 × 1 × 3 × 2 × 1 × 3 × 2 × 1 = 3! × 3! × 3!

where "!" represents the factorial operation, which is the product of all positive integers up to a given number.

So, the total number of different signals consisting of 9 flags that can be made using 3 white flags, 3 red flags, and 3 blue flags is:

3! × 3! × 3! = 6 × 6 × 6 = 216

Hence , the number of signals is 216

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Given Equations

Let it has solution (x,y)

Add both

\(\\ \sf\longmapsto 5x+4x+3y+7y=8+34\)

\(\\ \sf\longmapsto 9x+10y=42\)

It will also have same solution (x,y)

The solution of the equations is (-2, 6) which satisfies the equation 9x + 10y = 42.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of linear equations is given below.

5x + 3y = 8               ...1

4x + 7y = 34            ...2

From equation 1, then we have

5x + 3y = 8

y = 8/3 - (5/3)x

Put in equation 2, then we have

4x + 7[8/3 - (5/3)x] = 34

12x + 56 - 35x = 102

-23x = 46

x = - 2

Then the value of y is calculated as,

y = 8/3 - (5/3)(-2)

y = 8/3 + 10/3

y = 18 / 3

y = 6

Let's check whether (-2, 6) satisfy the equation 9x + 10y = 42 or not. Then we have

9(-2) + 10(6) = 42

- 18 + 60 = 42

42 = 42

The solution of the equations is (-2, 6) which satisfies the equation 9x + 10y = 42.

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\(f(x)=x\) for \(x\leq0\), therfore \(f(0)=0\).

the first domain is true for f(0) so we substitute value of x in the first function

\(f(x) = x \\ f(0) = 0\)

Answer:

irrational

Step-by-step explanation:

Since π is an irrational number, it would make 3π/9 an irrational number too since multiplying or dividing by pi makes the answer an irrational number.

Answer:

The solutions of the equation in the interval [0,2π )

                    ={  \(\frac{\pi }{3}\) }

General solution    θ = 2 nπ +α

                                θ =   \(2n\pi + \frac{\pi }{3}\)

Step-by-step explanation:

Step(i):-

Given equation

                      cos x + sin x tan x = 2

               ⇒      \(cos x + sin x \frac{sin x}{cos x} = 2\)

    On simplification , we get

              ⇒     \(\frac{sin^{2} x+ cos^2x}{cos x} = 2\)

we know that trigonometry formula

\(sin^{2} x+ cos^2 x = 1\)

now we get

             \(\frac{1}{cos x} = 2\)

⇒         \(cos x = \frac{1}{2}\)

⇒         cos x = cos 60°

Step(ii):-

General solution of cosθ = cosα

General solution    θ = 2 nπ +α

                               θ = 2 nπ +60°

                                θ =   \(2n\pi + \frac{\pi }{3}\)

put n = 0 ⇒ θ = 60°

Put n =1 ⇒  θ = 360°+60°= 420°

.....and so on

The solutions of the equation in the interval  =\(\frac{\pi }{3}\)

Final answer:-

The solutions of the equation in the interval [0,2π )

                    ={  \(\frac{\pi }{3}\) }

General solution    θ = 2 nπ +α

                                θ =   \(2n\pi + \frac{\pi }{3}\)

Answer:

havenche ai polld pener es quanto

Step-by-step explanation:

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

Answer:

50%

Step-by-step explanation:

6/12 students have taken fewer than 11 courses.

50% of students have taken fewer than 11 courses.

6/12=50/100

Step-by-step explanation:

4×sin(4t) = 4×sin(2t + 2t) =

= 4×(sin(2t)cos(2t) + cos(2t)sin(2t)) =

= 4×2×sin(2t)cos(2t) = 8×sin(2t)cos(2t)

but that did not lead anywhere near to any of the answer options.

so, i guess, you made typos in the description and in the answer options.

did you mean maybe

4×sin⁴(t) ?

sin⁴(t) = (3 - 4×cos(2t) + cos(4t))/8

4×sin⁴(t) = 4×(3 - 4×cos(2t) + cos(4t))/8 =

= (3 - 4×cos(2t) + cos(4t))/2 =

= 3/2 - 2×cos(2t) + 1/2 × cos(4t)

is that the real answer option 2 ?

then that is the correct answer.

Answer:

z= 168

Step-by-step explanation:

proportion zinc to copper = 4/17

4/17 = z/ 714

17 • z = 4 • 714

17 • z = 2856

z= 2856/17

z = 168

Answer:

60

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(5\sqrt[3]{x+8}=35\\ \\ \sqrt[3]{x+8}=7\\ \\ x+8=7^3\\ \\ x+8=343\)

Answer:

2

Step-by-step explanation:

Well if 2 are red it can only be either

rrrr

or

rrrw