Answer:
they pay $x*35.25
Step-by-step explanation:
this is the answer
Simplify the given expression. Write your answer with positive exponents. (x−4y3)−5
Answer: [tex]\frac{x^{20}}{y^{15}}[/tex]
This is the same as writing (x^20)/(y^15)
===================================================
Work Shown:
[tex]\left(x^{-4}y^3\right)^{-5}\\\\\left(x^{-4}\right)^{-5}*\left(y^3\right)^{-5}\\\\x^{-4*(-5)}y^{3*(-5)}\\\\x^{20}y^{-15}\\\\\frac{x^{20}}{y^{15}}[/tex]
In the second step, I used the rule that (a*b)^c = (a^c)*(b^c)
In step 3, I used the rule (a^b)^c = a^(b*c)
In the last step, I used the rule a^(-b) = 1/(a^b)
I DON'T UNDERSTAND THE ENGLISH OF THE QUESTION, WHAT IS 5-!?
Edit: I just realized the grey is part of the picture.
Answer:
The area of the small square is 1 cm^2
Step-by-step explanation:
The large square consist in four identical rectangles and one small square.
Then the area of the small square will be equal to the difference between the area of the large square and the areas of the rectangles.
Because we have 4 equal rectangles, if R is the area of one rectangle, and S is the area of the large square, the area of the small square will be:
area = S - 4*R
We know that the area of the large square is 49 cm^2
Then:
S = 49cm^2
Remember that the area of a square of side length K is:
A = K^2
Then the side length of the large square is:
K^2 = 49 cm^2
K = √(49 cm^2) = 7cm
And we know that the diagonal of one rectangle is 5cm.
Remember that for a rectangle of length L and width W, the diagonal is:
D = √(L^2 + W^2)
Then:
D = √(L^2 + W^2) = 5cm
And for how we construct this figure, we must have that the length of the rectangle plus the width of the rectangle is equal to the side length of the large square, then:
L + W = 7cm
L = (7cm - W)
Replacing this in the diagonal equation, we get:
√((7cm - W)^2 + W^2) = 5cm
(7cm - W)^2 + W^2 = (5cm)^2 = 25cm^2
49cm^2 - 14cm*W + W^2 + W^2 = 25cm^2
2*W^2 - 14cm*W + 49cm^2 = 25cm^2
2*W^2 - 14cm*W + 49cm^2 - 25cm^2 = 0
2*W^2 - 14cm*W + 24cm^2 = 0
We can solve this for W using the Bhaskara's formula, the solutions are:
W = [tex]\frac{-(-14)(+/-)\sqrt{14^{2}-4(2)(24) } }{2(2)}[/tex]
Then we have two solutions, and we only need one (because the length will have the other value)
We can take:
W = (14 cm + 2cm)/4 = 4cm
Then using the equation:
L + W = 7cm
L + 4cm = 7cm
L = 7cm - 4cm = 3cm
L = 3cm
Now remember that the area of one rectangle of length L and width W is:
R = L*W
Then the area of one of these rectangles is:
R = 4cm*3cm = 12cm^2
Now we can compute the area of the small square:
area = S - 4*R = 49cm^2 - 4*12cm^2 = 1cm^2
The area of the small square is 1 cm^2
This took me ages to complete so please brainliest
Out of all fan items sent for refurbishing, 40% had mechanical defects, 50% had electrical defects and 25% had both. Denote A="fan item has a mechanical defect" and B="fan item has an electrical defect". Determine the probability that a fan item selected at random will have at least one defect.
Using Venn probabilities, it is found that there is a 0.65 = 65% probability that a fan item selected at random will have at least one defect.
What is a Venn probability?In a Venn probability, two non-independent events are related with each other, as are their probabilities.
The "or probability" is given by:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In this problem, the given probabilities are [tex]P(A) = 0.4, P(B) = 0.5, P(A \cap B) = 0.25[/tex], hence, the "or probability", also called the "at least one" probability, is given by:
[tex]P(A \cup B) = 0.4 + 0.5 - 0.25 = 0.65[/tex]
0.65 = 65% probability that a fan item selected at random will have at least one defect.
More can be learned about Venn probabilities at https://brainly.com/question/25698611
Evaluate the integral. (Use C for the constant of integration.) 7x3 5x2 49x 5 (x2 1)(x2 7) dx
Answer:
[tex]\frac{7}{2}ln(|x^2+1|)+\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C[/tex]
Step-by-step explanation:
Perform the partial fraction decomposition
[tex]\int{\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)} } \, dx\\ \\\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{Ax+B}{x^2+1}+\frac{Cx+D}{x^2+7}\\ \\7x^3+5x^2+49x+5=(x^2+7)(Ax+B)+(x^2+1)(Cx+D)\\\\7x^3+5x^2+49x+5=Ax^3+Bx^2+7Ax+7B+Cx^3+Dx^2+Cx+D\\\\7x^3+5x^2+49x+5=Ax^3+Cx^3+Bx^2+Dx^2+7Ax+Cx+7B+D\\\\7x^3+5x^2+49x+5=x^3(A+C)+x^2(B+D)+x(7A+C)+7B+D[/tex]
Set up a system of equations and solve for each constant
[tex]\begin{cases} A + C = 7\\B + D = 5\\7 A + C = 49\\7 B + D = 5 \end{cases}[/tex]
[tex]A+C=7\\A=7-C[/tex]
[tex]7A+C=49\\7(7-C)+C=49\\49-7C+C=49\\49-6C=49\\-6C=0\\C=0[/tex]
[tex]A=7-C\\A=7-0\\A=7[/tex]
[tex]B+D=5\\B=5-D[/tex]
[tex]7B+D=5\\7(5-D)+D=5\\35-7D+D=5\\35-6D=5\\-6D=-30\\D=5[/tex]
[tex]B=5-D\\B=5-5\\B=0[/tex]
Plug solved constants in and evaluate
[tex]\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{Ax+B}{x^2+1}+\frac{Cx+D}{x^2+7}\\\\\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{7x+0}{x^2+1}+\frac{0x+5}{x^2+7}\\\\\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{7x}{x^2+1}+\frac{5}{x^2+7}[/tex]
Break up integral
[tex]\int {\bigr(\frac{7x}{x^2+1}+\frac{5}{x^2+7}\bigr) } \, dx[/tex]
[tex]\int {\frac{7x}{x^2+1} } \, dx +\int {\frac{5}{x^2+7}} \, dx\\\\\int {\frac{7x}{x^2+1} } \, dx +5\int {\frac{1}{x^2+7}} \, dx[/tex]
Solve first integral
Let [tex]u=x^2+1[/tex] and [tex]du=2xdx[/tex] for the first integral. Thus, [tex]\frac{7}{2}du=7xdx[/tex]:
[tex]\frac{7}{2}\int {\frac{du}{u}}\\\\\frac{7}{2}ln(|u|)+C\\ \\\frac{7}{2}ln(|x^2+1|)+C[/tex]
Solve second integral
Since [tex]5\int {\frac{1}{x^2+7} } \, dx[/tex] is in the form of [tex]\int{\frac{1}{x^2+a^2} } \, dx[/tex], its formula is [tex]\frac{1}{a}arctan(\frac{x}{a})+C[/tex]:
[tex]5\int {\frac{1}{x^2+7} } \, dx\\\\5\bigr(\frac{1}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C\bigr)\\\\\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C[/tex]
Combine integrals
[tex]\biggr[\frac{7}{2}ln(|x^2+1|)+C\biggr]+\biggr[\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C\biggr]\\ \\\frac{7}{2}ln(|x^2+1|)+\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C[/tex]
Tim purchases 3,000 shares in company X at $2.49 per share. The company subsequently announces a profit warning, and the share price drops to $2.24 per share. Wishing to minimise his losses, Tim decides to sell his shares. How much of a loss does Tim make? Give your answer in dollars to the nearest dollar
Answer:
$750
Step-by-step explanation:
Tim's share price changes by $2.24 -2.49 = -0.25, so the change in the value of his investment is ...
(3000 shares)(-0.25/share) = -$750
Tim takes a loss of $750 when he sells.
Answer:
Step-by-step explanation:
$\$1170$
Bob's initial investment is given by
Initial Investment =3,000×$1.25=$3,750.
When Bob sells the shares, he sells them for
Sold for price=3,000×$0.86=$2,580.
Therefore Bob's total LOSS is given by
Loss =$3,750−$2,580=$1,170.
Suppose that you have a data set of starting salaries and you find an average starting salary of $47,222 with a standard deviation of $6,528. There are 33 observations. What is the (estimated) standard error? Do not include a dollar sign and answer to two decimal places.
You were 20 inches tall at birth, and 65 inches tall on your 10th birthday. Create a linear equation to
represent this situation. According to your equation, how tall will you be at age 20?
Answer:
At age 20, you will be 90 in
Subtract 7a
2
-4ab+2b
2
from 3ab+7a2+2b2
Answer:
Step-by-step explanation:
3ab + 7a² + 2b² - (7a² - 4ab + 2b²) = 3ab + 7a² + 2b² - 7a² + 4ab - 2b²
Now combine like term. Like terms have same variable with same power.
= 3ab + 4ab + 7a² - 7a² + 2b² - 2b²
= 7ab
The cash price for a car was £7460. Mr Roberts bought the car on the
following hire purchase terms: A deposit of 20% of the cash price and 36 monthly payments of £191.60. Calculate the total amount Mr Roberts paid.
In 72,165 give the value of the
digit in the thousands place?
can someone please help me on my math please
Answer:
The answer is 112
Step-by-step explanation:
Area= base + base divided by 2 times height.
So 12+16 divided by 2 times 8.
What is the measure of the
hypotenuse of a right triangle
if the legs measure 10 and 24?
Answer:
hypotenuse= 26
Step-by-step explanation:
c= a^2 + b^2
10^2 + 24^2= 26
There are 76 milligrams of cholesterol in a 3.1 ounce serving of lobster. How much cholesterol is in 5 ounces of lobster
Answer:
123 milligrams
Step-by-step explanation:
76 : 3.1 = x : 5
76 * 5 = 3.1x
x = 76*5/3.1 = 123 milligrams
A shadow of a 4 foot pole is 10 feet long. A tower is 200 feet tall. What is the length of the shadow of the tower?
Answer:
27 feet
Step-by-step explanation:
We can set up a proportion comparing the height of each object to the length of the shadow.
h/s
h/15=18/10
Cross multiply.
10*h=18*15
10h=270
Use the multiplicative Inverse
10/10=270/10
h=27
Determine whether each number is a perfect square. If it is a perfect square, write
the number as a product of its two factors.
1.) 20
2.) 36
3.) 49
4.) 68
5.) 121
6.) 400
20 is not a perfect square.
36 = 6 times 6.
49 = 7 times 7.
68 is not a perfect square.
121 = 11 times 11.
400 = 20 times 20.
Hope this helps
helpp
helpp i need helpw tih thies
Answer:
20
Step-by-step explanation:
9/g+2h+5
g=3
h=6
=9/3+2(6)+5
=3+12+5
=20
hope dis helps.
pls brainliest!!!!!
Please help
( I will mark brainliest )
Answer:
umm i think A C D E ?
Step-by-step explanation:
because theyre all the same. some is just distribution. you should wait for another opinion though because im too lazy to check for B
Sal Boxer decided to divide a gift of $7000 into two different accounts. He placed $1000 in an account that earns an annual simple interest rate of 7.5%. The remaining money was placed in an account that earns an annual simple interest rate of 7.75%. How much interest will Sal earn from the two accounts after one year?
Answer:
Total yearly interest for the two accounts is: $570
Step-by-step explanation:
0.075*1000+0.0825*6000=570
75.0+495.0=570
Write a linear equation that passes through the points (-3, 3) and (9, -13) in standard form:
Answer:
4x +3y = -3
Step-by-step explanation:
The standard form equation can be written from ...
(y2 -y1)x -(x2 -x1)y = (y2 -y1)x1 -(x2 -x1)y1
(-13 -3)x -(9 -(-3))y = (-16)(-3) -(12)(3)
-16x -12y = 12
The standard form has a positive leading coefficient, and all terms mutually prime. We can get that by dividing the equation by -4:
4x +3y = -3
_____
Additional comment
The form we used above for the equation of the line essentially comes from the fact that the slope of a line is the same everywhere:
(y2 -y1)/(x2 -x1) = (y -y1)/(x -x1)
Multiplying by the product of denominators and separating variable terms from constant terms gives the form used above.
95×2 the answer to problem is
95 times 2 is 190.
90 times 2 is 180, and 5 times 2 is 10.
180 + 10 = 190.
work out the size of angles x, y and z.
Answer:
x = 41° , y = z = 74°
Step-by-step explanation:
x and 41 are alternate angles and are congruent , then
x = 41°
the 2 sides of the triangle with vertex = 32° are congruent so the triangle is isosceles with base angles being congruent , then
y = [tex]\frac{180-32}{2}[/tex] = [tex]\frac{148}{2}[/tex] = 74°
y and z are vertically opposite angles and are congruent so
z = 74°
Solve by factoring the quadratic equation 2x2 + 13x
=
-21.
Answer:
x = - [tex]\frac{7}{2}[/tex], x = - 3
Step-by-step explanation:
Given
2x² + 13x = - 21 ( add 21 to both sides )
2x² + 13x + 21 = 0 ← in standard form
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × 21 = 42 and sum = + 13
The factors are + 6 and + 7
Use these factors to split the x- term
2x² + 6x + 7x + 21 = 0 ( factor the first/second and third/fourth terms )
2x(x + 3) + 7(x + 3) = 0 ← factor out (x + 3) from each term
(x + 3)(2x + 7) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
2x + 7 = 0 ⇒ 2x = - 7 ⇒ x = - [tex]\frac{7}{2}[/tex]
Please show work
a. How many quarter-mile laps should Jim run to run 1 mile?
b. How many quarter-mile laps should Jim run to run 5 miles?
Group of answer choices
a. 5, b. 25
a. 3, b. 15
a. 4, b. 20
Answer:
a. 4, b.20
Step-by-step explanation:
There are 4 quarter mile laps in 1 mile, so you multiply the miles covered by 4 to find out the quarter mile laps.
a. 1x4=4
b. 5x4=20
Answer:
a. 4, b. 20
Step-by-step explanation:
A quarter mile is 1/4 a mile is 4/4 so if Jim runs 4 quarter miles he will run a mile so 4 is your answer. Since we know that a quarter mile is 1/4 and a mile is 4/4 we multiply 4*5 and get 20.
the number of people who have read a new book is 300 at the beginning of January. The number of people who read the book doubles each month. what do you notice about the difference in the number of people who read the book from month to month. what do you notice about the factor by which the number of people changes each month. if any people have read the book one month how many people read the book the following month.
At the end of the fourth month, we would have a total number of 4800 readers. The factor by which the number changes monthly is 2 and we would have 2n number of readers the following month
Data;
Initial Number of Readers = 300Factor of Increase 2The difference in number of people who read from month to monthThe difference in number of people who read from month to month will be
[tex]0 = 300\\1 = 2 * 300 = 600\\2 = 2 * 600 = 1200\\3 = 2 * 1200 = 2400\\4 = 2 * 2400 = 4800[/tex]
At the end of the fourth month, we would have a total number of 4800 readers.
The Factor by which the number changes monthlyThe factor by which the number changes monthly is 2. From the pervious calculation, we can see a constant increase by a factor of 2 month to month.
If n number of people are reading this month, the number of readers in the next month would be?Since we already established that the factor by which the readers increase is by two, we can simply say that at the next month, we would have 2n number of readers.
[tex]next month = 2 * n = 2n[/tex]
Learn more on linear equations here;
https://brainly.com/question/14323743
One day in the afternoon 3 groups of 8 students got 5 bags filled with pieces of candy.
they ate a certain amount of candy.
how much candy did each student eat?
work out (7×10^5) ÷ (2×10^2)
Answer:
3500 is the correct answer .Step-by-step explanation:
( 7×10^5) ÷ (2×10^2)= (7 × 100000) ÷ ( 2×100)= 700000 ÷ 200= 3500Mark BRAINLIEST
Thank you ☺️☺️
Translate the sentence into an equation:
three is 5 more than a number
Answer:
3=x+5
Step-by-step explanation:
Answer:
x + 5 = 3
Step-by-step explanation:
"Three is 5 more than a number."
The word is indicates that 3 is the final number, or rather, what the equation equals.
Then, 5 more than a number, shows the rest of your equation. A number is just your variable, so any letter. We'll use X. Then, it says that the answer (3) is 5 more than x. So, your equation is:
x + 5 = 3
1/2 of Cindy's money is equal to 2/3 of Emily's money. They have $105 altogether. How much money does each of them have?
Answer:
Cindy has $45 and Emily has $60
Step-by-step explanation:
let x be the amount of money , then
[tex]\frac{1}{2}[/tex] x + [tex]\frac{2}{3}[/tex] x = 105
multiply through by 6 ( the LCM of 2 and 3 ) to clear the fractions
3x + 4x = 630 , that is
7x = 630 ( divide both sides by 7 )
x = 90
Cindy has [tex]\frac{1}{2}[/tex] × 90 = $45
Emily has [tex]\frac{2}{3}[/tex] × 90 = $60
find 3 ratios
s that are equivalent to the given ratio 9 to 15
Answer:
3:5 & 18:30
Step-by-step explanation:
To find an equivalent ratio, just multiply or divide both terms by the same number. For the two I did, I divided by 3 for one, and multiplied by 2 for the other, but there are infinite possibilities. Hope this helped!
Solve |x -2.5| =8 please help
Answer (it has two solutions):
x = -5.5x = 10.5I hope this helps!