Mathematics College

How to solve this problem?

Answers

Answer 1

11)

x*y = -5*2 = -10, absolute value is 10

y*z = 2 * -2 = -4, absolute value is 4

10+4 = 14

Related Questions

If $3500 is invested at the rate of 8%, compounded quarterly, what will be the value of the investment 17 years from now, assuming no withdrawals?

Answers

We will use the compound interest formula, which is

A = P(1+r/n)^(n*t)

The variables are

A = amount in the account after t years
P = initial amount invested
r = interest rate (in decimal form)
n = compounding frequency
t = number of years

In this case

A = unknown (we're solving for this)
P = 3500
r = 0.08 (8% = 8/100 = 0.08)
n = 4 (compound quarterly ---> compound 4 times a year)
t = 17

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

Plug all these values into the equation to get...

A = P(1+r/n)^(n*t)
A = 3500(1+0.08/4)^(4*17)
A = 3500(1+0.02)^(4*17)
A = 3500(1.02)^(4*17)
A = 3500(1.02)^(68)
A = 3500(3.8442505025456)
A = 13454.8767589096
A = 13454.88

This means that you will have $13454.88 in the account after 17 years

Final Answer: 13454.88

What is the reciprocal of 2 2/3

Answers

[tex]\bf 2\frac{2}{3}\implies \cfrac{2\cdot 3+2}{3}\implies \cfrac{8}{3}\qquad reciprocal\implies \cfrac{3}{8}[/tex]

3/8, because you make the mixed number an improper fraction(8/3), then you flip it (3/8)

3 1/6 divided by 5/8

Answers

The result of 3 1/6 divided by 5/8 is equal to 76/15.

To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction.

In this case, 3 1/6 can be written as an improper fraction as (3 × 6 + 1) / 6 = 19/6.

Next, we can multiply the numerator of the fraction by the reciprocal of the divisor.

The reciprocal of 5/8 is 8/5.

So, (19/6) ÷ (5/8) = (19/6) × (8/5) = (19 × 8) / (6 × 5) = 152/30.

The fraction 152/30 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which in this case is 2. So, (152/30) ÷ 2 = 76/15.

Therefore, 3 1/6 divided by 5/8 is equal to 76/15.

Final answer:

To find the result of 3 1/6 divided by 5/8, convert the mixed number to an improper fraction, multiply by the reciprocal of the divisor, and simplify the resulting fraction. The answer is 5 1/15.

Explanation:

The student's question 3 1/6 divided by 5/8 is a mathematics problem that involves division of mixed numbers and fractions. To solve this problem, the student first needs to convert the mixed number into an improper fraction. To do this, the student multiplies the whole number by the denominator of the fractional part and then adds the numerator:

Multiply 3 (the whole number) by 6 (the denominator of the fractional part): 3 x 6 = 18.

Add the numerator (the fractional part's numerator, which is 1): 18 + 1 = 19. So, 3 1/6 becomes 19/6.

The next step is to divide 19/6 by 5/8. In division of fractions, you multiply by the reciprocal of the divisor. The reciprocal of 5/8 is 8/5.

Therefore, you multiply 19/6 by 8/5: 19/6 x 8/5.

Perform the multiplication of numerators and denominators: 19 x 8 = 152 and 6 x 5 = 30.

The result is 152/30. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

The simplified answer is 76/15, or as a mixed number, 5 1/15.

This shows that 3 1/6 divided by 5/8 is 5 1/15.

An animal shelter has a total of 350 animals comprised of cats, dogs, and rabbits. If the number of rabbits is 5 less than one-half the number of cats, and there are 20 more cats than dogs, how many cats are at the shelter?

Answers

This is the concept of algebra, suppose that the number of cats is x;
number of cats will be x-20
number of rabbits will be 3/2x
thus the total number of animals will be:
x+(x-20)+3/2x=350
7/2x=350+20
7/2x=370
x=370*2/7
x=105.7=106
therefore we conclude that there we 106 cats in the shelter

Final answer:

To find the number of cats at the animal shelter, we can set up and solve a system of equations using the given information. In this case, the number of dogs is 126 and the number of cats is 146.

Explanation:

To solve this problem, let's assign variables to represent the number of cats, dogs, and rabbits at the shelter. Let's say the number of cats is 'c', the number of dogs is 'd', and the number of rabbits is 'r'.

From the given information, we can form three equations:

The total number of animals is 350: c + d + r = 350The number of rabbits is 5 less than one-half the number of cats: r = (1/2)c - 5There are 20 more cats than dogs: c = d + 20

Using these equations, we can solve for the value of 'c' (the number of cats).

By substituting the value of 'c' from equation 3 into equation 2, we get:

r = (1/2)(d + 20) - 5

Now, we substitute the values of 'c' and 'r' from equations 3 and 1 into equation 1:

(d + 20) + d + ((1/2)(d + 20) - 5) = 350

Simplifying this equation, we get:

2d + (1/2)d + 35 = 350

Combining like terms, we have:

4d + d + 70 = 700

Simplifying further, we find:

5d + 70 = 700

Subtracting 70 from both sides of the equation, we get:

5d = 630

Dividing both sides by 5, we find that d = 126. Therefore, there are 126 dogs at the shelter.

Finally, by substituting the value of d back into equation 3, we find:

c = 126 + 20 = 146. Thus, there are 146 cats at the shelter.

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i need to know the solution using a fraction or integer to 3 more than the product of 7 and a number x is less than 26

Answers

so.. the number is "x", now, the product of "x" and 7 is just 7*x or 7x.

3 more than that? is just 7x + 3

so, we know is less than 26, 7x + 3 < 26

[tex]\bf 7x+3\ \textless \ 26\implies 7x\ \textless \ 26-3\implies 7x\ \textless \ 23\implies x\ \textless \ \cfrac{23}{7} \\\\\\ \boxed{x\ \textless \ 3\frac{2}{7}}\qquad \qquad 3\frac{2}{7}\implies \cfrac{3\cdot 7+2}{7}\implies \cfrac{23}{7}[/tex]

Anoav uses which statistical distribution to determine the significance of the results

Answers

In statistics, ANOVA means Analysis of Variance. This is a statistical tool that helps in determining if the effect of the independent variable on the dependent variable is significant or not. It uses the F-distribution to determine the difference of means. That is why the other name for ANOVA is the F-test. It was named in honor of Ronald Fisher. It is a table consisting of F values which is simply the ratio of two variances. It depends on the degrees of freedom and the α to be used. A sample of the F-table is shown in the picture.

A new basketball costs $25.00 at the sporting goods store. If the store is having a going-out-of-business sale and everything is 60% off, what is the actual cost of the basketball?

Answers

Final answer:

To calculate the discounted price of the basketball, multiply the original price ($25.00) by 60% to find the discount ($15.00), and subtract this from the original price to get the final price ($10.00).

Explanation:

To find out the actual cost of the basketball after a 60% discount, we start by calculating the amount of the discount. A 60% discount on a $25.00 basketball means the discount is 60/100 times $25.00. To do the calculation:

First, we convert the percentage to a decimal: 60% = 0.60.Then, we multiply the original price by the decimal: $25.00 × 0.60 = $15.00.This $15.00 is the amount of the discount.

To find the discounted price, we subtract the discount from the original price: $25.00 - $15.00 = $10.00. Therefore, the discounted price of the basketball is $10.00.

Between 2005 and 2008, the average rate of inflation was about3.4 per year. If a cart of groceries cost $140 in 2005, what did it cost in 2008

Answers

The formula is
A=p (1+r)^t
A future value?
P current value 140
R rate of inflation 0.034
T time 2008-2005=3 years
A=140×(1+0.034)^(3)
A=154.77 round your answer to get
A=155

Find the surface area of x^2+y^2+z^2=9 that lies above the cone z= sqrt(x^@+y^2)

Answers

The cone equation gives

[tex]z=\sqrt{x^2+y^2}\implies z^2=x^2+y^2[/tex]

which means that the intersection of the cone and sphere occurs at

[tex]x^2+y^2+(x^2+y^2)=9\implies x^2+y^2=\dfrac92[/tex]

i.e. along the vertical cylinder of radius [tex]\dfrac3{\sqrt2}[/tex] when [tex]z=\dfrac3{\sqrt2}[/tex].

We can parameterize the spherical cap in spherical coordinates by

[tex]\mathbf r(\theta,\varphi)=\langle3\cos\theta\sin\varphi,3\sin\theta\sin\varphi,3\cos\varphi\right\rangle[/tex]

where [tex]0\le\theta\le2\pi[/tex] and [tex]0\le\varphi\le\dfrac\pi4[/tex], which follows from the fact that the radius of the sphere is 3 and the height at which the sphere and cone intersect is [tex]\dfrac3{\sqrt2}[/tex]. So the angle between the vertical line through the origin and any line through the origin normal to the sphere along the cone's surface is

[tex]\varphi=\cos^{-1}\left(\dfrac{\frac3{\sqrt2}}3\right)=\cos^{-1}\left(\dfrac1{\sqrt2}\right)=\dfrac\pi4[/tex]

Now the surface area of the cap is given by the surface integral,

[tex]\displaystyle\iint_{\text{cap}}\mathrm dS=\int_{\theta=0}^{\theta=2\pi}\int_{\varphi=0}^{\varphi=\pi/4}\|\mathbf r_u\times\mathbf r_v\|\,\mathrm dv\,\mathrm du[/tex]
[tex]=\displaystyle\int_{u=0}^{u=2\pi}\int_{\varphi=0}^{\varphi=\pi/4}9\sin v\,\mathrm dv\,\mathrm du[/tex]
[tex]=-18\pi\cos v\bigg|_{v=0}^{v=\pi/4}[/tex]
[tex]=18\pi\left(1-\dfrac1{\sqrt2}\right)[/tex]
[tex]=9(2-\sqrt2)\pi[/tex]

A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for football or baseball. Out of the total 77 people who liked football, 48 also liked baseball. There were 65 people who liked baseball. Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points) Like football Do not like football Total Like baseball A D G Do not like baseball B E H Total C F I Part B: What percentage of the survey respondents did not like either football or baseball? (3 points) Part C: Do the survey results reveal a greater dislike for football or baseball? Justify your answer. (2 points)

Answers

PART A:

Total of students who like football = 77 students
Students who like football and baseball = 48 students
Students who like football and not baseball = 77 - 48 = 29 students

Students who do not like football = 100 - 77 = 23 students

Students who like baseball = 65 students
Students who like baseball but not football = 65 - 48 = 17 students

Students who do not like baseball = 100 - 65 = 35 students

These data can be represented in a two ways table as shown below

PART B:

The number of students who do not like either football or baseball is 29+17+6=52

The probability is 52/100 = 52%

PART C:

The number of students who don't like football is 17+6=23 students
The number of students who don't like baseball is 35 students

The survey result reveals a greater dislike for baseball

The equation d=13/v shows that the density of a particular substance equals a mass of 13 grams divided by the volume of the substance. What happens to the density as the volume approaches 0?

Answers

d = M/V where M=mass and V = volume

Assume the Mass is 1 kg and the Volume = 1 cm³, so d= 1/1 kg/cm³

for V=0.1 → d = 1/0.1 = 10 kg.cm³
for V = 0.01 → d = 100.kg.cm³
for V = 0.001 → d = 1000.kg.cm³
for V = 0.000001 → d = 1,000,000.kg.cm³
and when Volume → 0. density →∞
.

Answer: the density approaches infinity

Step-by-step explanation:

Kurt wants to have $25,000 in an investment account four years from now. the account will pay 0.2 percent interest per month. if he saves money every month, starting one month from now, how much will he have to save each month to reach his goal

Answers

Given:
F = 25000, future value
i=0.02 per month, compounded monthly
n=4*12=48 periods (months)
Need A=monthly deposit

The amount A is given by the formula
A=Fi/((1+i)^n-1) [can be derived from the annuity formula]
=25000*0.02/((1.02^48-1)
= 315.05

Answer: Kurt will need to save $315.05 each month to reach the goal of saving $25000 after 4 years.

Kurt will have to save an amount of $496.75 each month.

What is Compound Interest?

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

Final amount of the account, A = $25,000

Interest rate, r = 0.2% = 0.002

Number of years, t = 4 years

Interest compounded monthly, so n = 12

Annuity can be found using the formula,

Annuity = 25,000 ÷ {[(1 + 0.002)^(12×4) - 1] / 0.002}

= 25,000 ÷ {[(1.002)⁴⁸ - 1] / 0.002}

= 496.75

Hence the amount Kurt needs to save each month is $496.75.

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Jim drove 204 miles in 4 hours. If he can keep the same pace how long will it take him to drive 918 miles

Answers

18 hours.

Proportions and stuff.

[tex] \frac{204}{4} [/tex] = [tex] \frac{918}{x} [/tex]

Cross multiply,

204x = 918 * 4

204x = 3672
/204 /204
x = 18

18 hours.

Consider the following.
Point
(-5, 4)
Line
x + y = 7
(a) Write the slope-intercept form of the equation of the line through the given point and parallel to the given line.

(b) Write the slope-intercept form of the equation of the line through the given point and perpendicular to the given line.

Answers

x + y = 7....y = -x + 7....the slope here is -1

A. a parallel line will have the same slope
y = mx + b
slope(m) = -1
(-5,4)...x = -5 and y = 4
sub and find b, the y int
4 = -1(-5) + b
4 = 5 + b
4 - 5 = b
-1 = b
so ur parallel line is : y = -x - 1 <==

B. perpendicular lines have negative reciprocal slopes. That means our perpendicular line will have a slope of 1
y = mx + b
slope(m) = 1
(-5,4)...x = -5 and y = 4
now we sub and find b, the y int
4 = 1(-5) + b
4 = -5 + b
4 + 5 = b
9 = b
so ur perpendicular line is : y = x + 9 <==

(03.03 HC)

The table shows the outputs, y, for different inputs, x:

Input (x) 6 12 15 25
Output (y) 14 15 15 16

Part A: Do the data in this table represent a function? Justify your answer. (3 points)

Part B: Compare the data in the table with the relation f(x) = 7x − 15. Which relation has a greater value when x = 6? (2 points)

Part C: Using the relation in Part B, what is the value of x if f(x) = 6? (5 points)

Answers

part A the table does not show function because 15 is repeated which is a relationship.

The scatter plot below shows the relationship between the length (x) in meters and mass f(x) in kg of a marine animal
(1,0)(2,10)(3,20)(4,30)(5,40)(6,50)(7,65)(8,70)(9,80)(10,90)

Which of the following fuction is best represented by the scatter plot?
F(x)=9-10.3x
F(x)=-10.3+9x
F(x)=-9+10.3x
F(x)=10.3-9x

Answers

F(x) = -9 + 10.3x probably.
It's definitely not the first or last option as they have negative gradients (i.e. negative x-coefficient) and so represent a negative correlation. The data given tells us there is a positive gradient and so a positive correlation.
It could be the second option as the second and third are not so vastly different but I would go for the third because it appears to most closely fit the data pattern.

Answer:

F(x)=-9+10.3x

Step-by-step explanation:

Given:

(1,0)

(2,10)

(3,20)

(4,30)

(5,40)

(6,50)

(7,65)

(8,70)

(9,80)

(10,90)

F(x)=9-10.3x and F(x)=10.3-9x cannot be the function of given scatter plot since the slope in these functions are negative

So, The equation of line can be F(x)=-10.3+9x or F(x)=-9+10.3x

Refer the attached figure.

Using desmos calculator

We conclude that the function is best represented by the scatter plot is [tex]F(x)=-9+10.3x[/tex]

Which of the following is closest to 27.8 times 9.6? A. 280. B 300. C 2,800. D 3,000

Answers

A 280. you really couldn't use a calculator?

The answer would be A because multiplying the 2 numbers give you 266.88

a garden table and a bench cost 817 dollars combined. The garden table costs 83 less than the bench. what is the cost of the bench

Answers

table=t
bench=b

t=b-83

t+b=817
b-83+b=817
2b=900
b=450 ($)

"Non nobis, Domine, non nobis, sed Nomini tuo da gloriam."

Regards M.Y.

Find The Perimeter Of The Shaded Region

90 ft
58 ft
24 ft
38 ft

Answers

l = 14 - 6 = 8
w = 15 - 4 = 11

P of shaded = 2(8+9) = 2 (19) = 38

answer
last one 38ft

Answer:

38 ft

Step-by-step explanation:

Perimeter of the rectangle = 2* length + 2* width

Length of shaded part = Length of the larger rectangle - 4 = 11ft

width of the shaded part = width of the larger rectangle - 6 = 8 ft

Perimeter of the rectangle = 2* length + 2* width

Plug in the values of length and width

Perimeter of the shaded rectangle= 2(11) + 2(8)= 22+ 16= 38 feet

Suppose a least-squares regression line is given by modifyingabove y with caret equals 4.302 x minus 3.293y=4.302x−3.293. what is the mean value of the response variable if x equals 20x=20

Answers

Final answer:

The mean value of the response variable y when x equals 20 in the least-squares regression line equation y = 4.302x - 3.293 is 82.041.

Explanation:

The given equation is y = 4.302x - 3.293, which is a least-squares regression line. In this formula, x is the independent variable and y is the resulting dependent variable or response. The goal is to find the mean value of the response variable when x is 20. This can be achieved simply by plugging 20 in place of x in our equation and calculating the resulting value for y.

We will substitute x = 20 into the equation y = 4.302x - 3.293. Therefore, the value of y when x is 20 is:

y = 4.302(20) - 3.293 = 82.041

So, when x = 20, the mean value of the response variable y or the predicted y value is 82.041.

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Two trains leave a train station traveling different directions. The first train travels 12 miles west, then 6 miles north. The second train travels 20 miles east, then 35 miles north.
a. The train station is the origin. What is the coordinate of each train?
b. Using the city center and the stop point of the first train, what is the slope of the line? Is it horizontal, vertical or neither? Write the equation of the line in slope-intercept form and standard form.
c. The city wants to build a train station 2 miles directly north of the first train station. They are going to build a train track parallel to the path the first train would’ve traveled if it were a direct route from the city center. What would be the equation of the line in slope intercept form of the new track?

Answers

Draw a diagram to illustrate the problem as shown below.
The origin (0, 0) is the train station.

Part a.
The first train travels 12 miles west and 6 miles north to arrive at A.
It's coordinate is (-12, 6).

The second train travels 20 miles east and 35 miles north to arrive at B.
It's coordinate is (20, 35).

Part b.
The slope of the line from the origin to A is
m = (6 - 0)/(-12 - 0) = -1/2.
The slope is neither vertical nor horizontal.
The y-intercept is 0.

The line OA is given in slope-intercept form by
y = -(1/2)x
In standard form, the line is
y - 6 = -(1/2)*(x - (-12))
or
y - 6 = -(1/2)*(x + 12)

Part c.
The new train station is located at (0, 2) because it is 2 miles north of the old station.
If a new track is built parallel to OA, then it should have a slope of -1/2.
Because it's y-intercept is 2, its equation in slope-intercept form is
y = -(1/2)x + 2.

Answer:a. first (-12,6) second (20,35)

b. y = -1/2x, 2y + 1x = 0 (neither horizontal or vertical)

c. y= -1/2x + 2.

Step-by-step explanation:

Two people are traveling and need to exchange the currency of their native country for the currency of the country they are visiting. drag each exchange to match the ratio of currency to currency in each category.

Answers

Answer:

The solution is shown in attached figure.

Step-by-step explanation:

In table 1,