Evaluate the polynomial xyz^2-z when x=6, y=-4, and z=-2

The perimeter of a rectangle is 10(y-1).

Option (c) is correct.

It is required to find the expression of perimeter of a rectangle.

A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.

Given that:

Let the length of rectangle be 3y-5

Let the breadth of rectangle be 2y

As we know the formula for perimeter,

So,

Perimeter (P)= 2Length (L) +2Width (W)

P=2L + 2W

P=2(2y)+2(3y-5)

P=4y+6y-10

P=10y-10

∴P=10(y-1)

Therefore, the perimeter of a rectangle is 10(y-1).

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To find the initial deposit (P) of Francisco's savings account, we can use the compound interest formula P = A / (1 + r/n)^(nt) with the given values, leading to P = 2,033.88 / (1 + 0.029/12)^(12*9) and solve for P.

To determine the value of Francisco's initial deposit in a savings account that has grown to $2,033.88 with an interest rate of 2.9% compounded monthly after nine years, we need to use the formula for compound interest:

P = A / (1 + r/n)^(nt)

Where:

Given:

Substituting the given values into the formula, we get:

P = 2,033.88 / (1 + 0.029/12)^(12*9)

After calculating the above expression, we can find the initial deposit Francisco made into his savings account nine years ago.

Final answer:

Francisco initially deposited approximately $1,511.29 into the savings account.

Explanation:

To find out how much money Francisco initially deposited, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount ($2,033.88)

P is the principal (initial deposit)

r is the interest rate per period (2.9% or 0.029 in decimal form)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years (9)

Plugging in the values, we can solve for P:

2,033.88 = P(1 + 0.029/12)^(12*9)

Simplifying the expression:

2,033.88 = P(1.002416667)^108

2,033.88 = P(1.343917334)

P = 2,033.88 / 1.343917334

P ≈ $1,511.29

Therefore, Francisco initially deposited approximately $1,511.29 into the savings account.

The final sale price of phone after mark-down of 15% is $169.15

The selling price is defined as a price after the original price has been increased or decraesed.

Original price was $199.

Marked down 15% ==$199x 0.15 = $29.85

Final sale price after mark-down of 15% = $199 - $29.85 = $169.15

Hence, the final sale price of phone after mark-down of 15% is $169.15

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Answer: 35 minutes

Step-by-step explanation:

Given : Jess spent 7x minutes on the computer.

Her sister spent 5 x + 10 minutes on the computer, which was the same amount of time Jess spent.

Thus , we have

[tex]7x=5x+10[/tex]

Subtract 5x from both the sides , we get

[tex]2x=10[/tex]

Divide both sides by 2, we get

[tex]x=5[/tex]

Now, the time spent by Jess = 7(5)=35 minutes

Hence, Jess was 35 minutes on computer.

Final answer:

To find the number of students who are not freshmen, we first calculate the total number of students using the percentage of freshmen and then subtract the number of freshmen from the total.

Explanation:

The student's question is asking for the total number of students at Grandy High School given that 35% of the students are freshmen and there are 525 freshmen. To find the total number of students, we can use the percentage formula:

Determine the percentage that the freshman represent: 35%.

Recognize that the 525 freshmen is 35% of the total. So, if 35% is 525, we can set up the equation: 0.35 × Total Number of Students = 525.

Divide both sides by 0.35 to find the total number of students: Total Number of Students = 525 ÷ 0.35.

Calculate the total number of students: Total Number of Students = 1500.

Since 35% are freshmen, the remaining 65% are not freshmen. Now, calculate 65% of the total students: 0.65 × 1500 = 975.

Therefore, 975 students are not freshmen.

Answer:

B. 1

Step-by-step explanation:

just got it right on edge

The maximum value of y = cos(θ) for values of θ between -720° and 720° is 1.

The cosine function has a maximum value of 1 when the angle is 0 degrees or 360 degrees (or any integer multiple of 360 degrees).

In the given range of θ between -720° and 720°,

It can be seen that -720° and 720° are integer multiples of 360 degrees.

Therefore, the maximum value of y = cos(θ) for values of θ between -720° and 720° is 1.

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Answer:

6.5

Step-by-step explanation:

To perform this kind of exercise, it is necessary to replace the value indicated in each variable each time you find the variable in the equation.

[tex]7j+5-8k[/tex]

If j=0.5 and k=0.25, replace the value of each variable.

[tex]7(0.5)+5-8(0.25)=[/tex]

now perform the indicated operations

[tex]7(0.5)+5-8(0.25)=3.5+5-2=6.5[/tex]

Answer:

6.5

Step-by-step explanation:

There are a total of 40 weeks in 280 days.

Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that there are 7 days in 1 week and some months consist of 30 days. Now, the number of weeks that 280 days will have can be found as,

Number of weeks = Total number of days / Number of days in a week

                              = 280 days / 7 days per week

                              = 40 week

Therefore, There  are 40 weeks in 280 days.

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Answer:

72º

Step-by-step explanation:

In order to calculate this you have to remember that the center angle of any polygon measures 360º, so what we do is just divide those 360 by the number of angles that you will find in the polygon, the number of angles equals the number of sides, so the pentagon has 5 sides, it will also have 5 angles. So we just divide the 360/5=72

So the smallest angle of rotational symmetry that maps a regular pentagon onto itself will be 72º

The required property is associative property.

Given that,
To determine a property of addition is shown in the following number sentence 7+(3+5)=(7+3)+5.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
7 + (3 + 5) = (7 + 3) + 5
Here, accoding to the PEMDAS rule, in mathematical string solution of the parenthesis is on priority. But we can see here on the left we add first 3 and 5 then the product adds to 7 and on the right, we add first 7 and 3 then the product adds to 5 gives the same result, this property of addition of number is called associative property.
As
7 + (3 + 5) = (7 + 3) + 5
7 + 8 = 10 + 5
15 = 15

Thus, the required property is associative property.

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Answer:

Step-by-step explanation:

Let the other be [tex] = x[/tex]

As the sum of the number is given as [tex] \frac {7}{8}[/tex]

And one number is [tex] \frac{3}{4}[/tex]

According to question

[tex] \frac{3}{4} +x = \frac{7}{8}[/tex]

Subtracting [tex] \frac{3}{4}[/tex] from both sides we get

[tex] \frac{3}{4} +x - \frac{3}{4} = \frac{7}{8} - \frac{3}{4}[/tex]

Taking LCM of 4 and 8 we get 8

And making

[tex] \frac{3}{4} [/tex] and [tex]\frac{7}{8}[/tex] like fraction by making denominator same.

Multiply [tex] \frac{3}{4} [/tex] by 2 in numerator and denominator and multiply [tex]\frac {7}{8}[/tex] by 1 in numerator and denominator we get

[tex]x= \frac{7}{8} - \frac{6}{8}[/tex]

[tex]x= \frac{7-6}{8}[/tex]

[tex]x =\frac{1}{8}[/tex]

Hence, the other number is [tex]\frac{1}{8}[/tex]

The normal time for this operation is approximately 8.333 seconds. Charlene Brewster is performing at a similar speed to the average for this operation.

The question provides the lap times for Charlene Brewster as 8.4, 8.6, 8.3, 8.5, 8.7, and 8.5, with a performance rating of 110%. To find the normal time for this operation, we can calculate the average of the lap times. Adding all the lap times together and dividing by the number of laps, we get (8.4 + 8.6 + 8.3 + 8.5 + 8.7 + 8.5) / 6 = 50 / 6 = 8.333. Therefore, the normal time for this operation is approximately 8.333 seconds.

Comparing the normal time to Charlene's lap times, we see that her lap times are relatively close to the normal time. This indicates that she is performing at a similar speed to the average for this operation.

The comparison sentence that best represents the equation 6 x 7 = 42 is option 3) 42 is 6 times as many as 7.

Let's break it down step-by-step:

Therefore, the correct choice is option 3) 42 is 6 times as many as 7.

The probability that less than 40% of the 80 voters surveyed indicate they voted for candidate A is P(phat <0.4) = P((phat-p)/sqrt(p*(1-p)/n) <(0.4-0.43)/sqrt(0.43*(1-0.43)/80)) =P(Z<-0.542) =0.2939 (from standard normal table)

Answer:

29.46% probability that less than 40% of the 80 voters surveyed indicate they voted for candidate a

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

For a proportion p in a sample of size n, we have [tex]\mu = p, \sigma = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this problem, we have that:

[tex]\mu = 0.43, \sigma = \sqrt{\frac{0.43*0.57}{80}} = 0.05535[/tex]

What is the probability that less than 40% of the 80 voters surveyed indicate they voted for candidate a?

This is the pvalue of Z when X = 0.4. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{0.4 - 0.43}{0.05535}[/tex]

[tex]Z = -0.54[/tex]

[tex]Z = -0.54[/tex] has a pvalue of 0.2946

29.46% probability that less than 40% of the 80 voters surveyed indicate they voted for candidate a