Answer:
80 grams of butter
Step-by-step explanation:
640/2=329
3x320=960
960-880=80
Tunde and Martha are married and share their income. Tunde earns $1,500 per year less than Martha. If their annual income is $47,500, how much does each earn?
Answer:
p=2m
p+m=51
take the 2m and plug that in for p -> 2m+m=51
3m=51
m=51/3
m=17 then plu the value of m into Paula's points
p=2(17)
p=34
Helen has 48 cubic inches of clay to make a solid
square right pyramid with a base edge measuring 6
inches.
Which is the slant height of the pyramid if Helen uses all
the clay?
O 3 inches
O4 inches
O 5 inches
O 6 inches
6 in
Save and Exit
Next
Submit
Mark this and return
Answer:
4 inches.
Step-by-step explanation:
The formula for the volume of a pyramid is v=1/3bh.
V is the volume of the shape
1/3 is just a rational number or fraction.
b is the area of the base shape of the 3d shape
h is the height of the shape (slant height).
The general formula for the volume of all shapes is V=Bh
V is the volume
B is the area of the base
h is the height of the prism.
In this case, we have a pyramid, so let's use the formula V=1/3Bh.
We know what the volume so 48=?
We can put 1/3 so 48=1/2 times ? times ?.
The base shape of this pyramid is a square, and it has an edge of 6 inches. We need to find the area of that square because it is the area of our base. the formula for finding the area of a square is A=S squared.
A is the area of the shape
S is the side length.
The reason why it is squared is because all sides of a square are equal to each other. Since the base edge is 6 inches, the other edges are 6 inches as well. There are 4 edges in a square.
A= 6 times 6.
A=36.
We have the area of the base, so we can put 48=1/3 times 36 times ?.
We are finding what the slant height is, so let's put the letter "h" to represent the slant height.
Now, 48=1/3 times 36 times h.
All we have to do is solve for h.
First we have to simplify one side of the equation.
To simplify, we have to do 1/3 times 36, or you can do 36 divided by 3. It is your choice. 36 divided by 3 is 12.
Now we have 12h=48.
Isolate h by dividing both sides by 12. 12h divided 12 is h. 48 divided by 12 is 4.
Therefore h=4 inches. The reason we divide both sides is because we have to do the inverse operation of the original equation. For instance 12h=48. To get to 48, you do 12 times h. We take the inverse (opposite) operation of multiplication (division). That will isolate for h.
The slant height of this square pyramid is 4 inches.
Hope this helps. Have a good rest of your day!
The slant height of the pyramid is 4 inches. Therefore, the option B is the correct answer.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, volume of square right pyramid = 48 cubic inches and base edge measuring 6 inches.
We know that, the volume of square based pyramid =a²h/3.
Here, a=6 inches and h=slant height
Now, 48= (6²×h)/3
48=36h/3
48=12h
h=4 inches
Therefore, the option B is the correct answer.
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i need help emergrncy shots fire shots fire we neeed all back ups
Answer:
a = 9h + bn
Step-by-step explanation:
total = $9 an hour + (bonus x number of items repaired)
A spinner has 4 equal sectors with tour options Dubai, Seoul, Switzerland, and Paris. What is the probability of landing on Seoul or Paris after spinning spinner
The probability of landing on Seoul or Paris after spinning spinner is 1/2 .
What is Probability ?Probability is the measure of likeliness of an event to happen.
It is given that
Total Outcomes = 4 ( Dubai, Seoul, Switzerland, and Paris)
the probability of landing on Seoul or Paris after spinning spinner = ?
The probability of Landing on Seoul P(S) is 1 /4
The probability of Landing on Paris P(P) is 1 /4
The probability of landing on Seoul or Paris after spinning spinner is
P( S∪P) = P(S) + P(P)
= (1/4) + (1/4)
= 1/2
Therefore , The probability of landing on Seoul or Paris after spinning spinner is 1/2 .
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This function to calculate the area of a rectangle is not very readable. Can you refactor it, and then call the function to calculate the area with base of 5 and height of 6? Tip: a function that calculates the area of a rectangle should probably be called rectangle_area, and if it's receiving base and height, that's what the parameters should be called.
Answer:
Here is the refactored function:
def rectangle_area(base, height):
area = base * height
return area
print("The area is ", rectangle_area(5,6))
Step-by-step explanation:
The above program has a function rectangle_area that takes two variables base and height as parameters. The function then computes the area of rectangle by multiplying the values of base and height. The result of the multiplication is assigned to the variable area. Then the function returns the resultant area.
print("The area is ", rectangle_area(5,6)) statement calls rectangle_area() method by passing values of base and height i.e. 5 and 6 to compute the area. The output of this program is:
The area is 30
Note that the use of rectangle_area function name describes what the function does i.e. it computes the area of rectangle. By naming the parameters as base and height that clearly depicts that in order to compute rectangle are we need the base and height of rectangle. So this makes the code readable.
Solve the equation for X. 2(2x-4)=3(x+4) A -4 B 4 C 20 D 6
Answer:
X=20
Step-by-step explanation:
The answer is C
A tower is 40 ft tall and 20 ft wide. A model of the tower is 5 in. tall. Identify the width of the model in inches.
Answer:
The width of the model will be 2.5 inches
Step-by-step explanation:
The tower was scaled down by a factor to a smaller size in the model. We are to, first of all, determine this factor and then use it to scale down the width of the model.
Step One: Determine the scale factor from the tower height.
The scale factor is obtained from the formula:
Scale factor = model size / observed size
This will be
Height of model tower/ height of the real tower.
The height of the model tower is 5 inches which is the same as 0.416667 ft
Scale factor = 0.416667 ft/ 40ft = 0.0104
Step two: Multiply the width of the real-life tower by the scale factor to get the model width.
Width of model =20ft X 0.0104 = 0.208ft
Step three: Convert your answer back to inches.
We will now have to convert 0.208 ft back to inches by multiplying by 12
This will be 0.208 X 12 =2.5 inches.
The width of the model will be 2.5 inches
Which statements are true rega quadrilateral. ABCD? ABCD has congruent diagnals
Answer:
the first, second and last option are all correct
Step-by-step explanation:
just Googled and squares have congruent diagonals, and the definition of a rhombus is that all the sides and angles have to be equal and adjacent, and a square has those qualities, which would also make the last statement true.
a square have two pairs of parallel sides, making the fourth one incorrect
and a square is also a rectangle so the third one is wrong as well!! :)
75% letter size paper and 25% legal size paper. What is the ratio of letter size paper to legal size paper
Answer:
3:1
Step-by-step explanation:
75%=[tex]\frac{75}{100}[/tex]=[tex]\frac{3}{4}[/tex]
25%=[tex]\frac{25}{100}[/tex]=[tex]\frac{1}{4}[/tex]
A certain variety of pine tree has a mean trunk diameter of y = 150 cm and a
standard deviation of o = 30 cm.
A certain section of a forest has 500 of these trees.
Approximately how many of these trees have a diameter smaller than 120 cm?
Answer:
80 trees have a diameter smaller than 120cm
Step-by-step explanation:
Step 1
To solve this question, we would make use of the Z score formula.
z = x - μ/σ
Where
z = z score
x = Raw score = 120cm
μ = Population mean = 150cm
σ = Population standard deviation = 30cm
Hence,
z =120 - 150/30
z = -1
The z score = -1
Step 2
We find the Probability of the calculated z score using the z score table.
P(z) = P(z = -1) = P(x<120) = 0.15866
Approximately to the nearest hundredth = 0.16
Converting to percentage = 0.16 × 100 = 16%
The percentage of trees with a diameter smaller than 120cm = 16%
Therefore, the number of trees with a diameter smaller than 120cm
= 16% × 500 trees = 80trees
Write the equation of the function of a parabola with vertex at (–1,–2) and a point (1,–6) that lies on the curve.
Answer:
f(x) = -(x + 1)² - 2
Step-by-step explanation:
f(x) = a(x - h)² + k
-6 = a(1 - -1)² + -2
-6 = a(4) -2
-4 = 4a
a = -1
f(x) = -(x + 1)² - 2
What is the average rate of change of f(x)=-2/x^2 when the interval is 1 to 2
Answer:
1.5
Step-by-step explanation:
average rate of change = (f(x2) - f(x1))/(x2 - x1)
f(x) = -2/x^2
f(x2) = f(2) = -2/(-2)^2 = -2/4 = -0.5
f(x1) = f(1) = -2/1^2 = -2
average rate of change = (-0.5 - (-2))/(2 - 1)
average rate of change = (-0.5 + 2)/1
average rate of change = 1.5
(a) The only even prime number is ....
Answer:
2 is the only even prime number
Answer:
2
Step-by-step explanation:
2 is the only even prime number. There is no even prime number other than 2. Prime numbers are the numbers which can only be divided by 1 and the number itself.
Which equation represents the line that is parallel to y=4 and passes through (-3,1).
A. x=1
B. x= 3
C. y= 1
D. y= 4x + 13
Answer:
C. y = 1
Step-by-step explanation:
For two line to be parallel, they have to have the same slope. The slope for the equation y = 4 is 0. This cancels out answer choices A, B, and D.
A and B have an undefined slope since they are vertical lines.
D has a slope of 4.
Also, the line has to go through the point (-3, 1). Since the line has a slope of 0, the equation will include the y-value. The y-value for this point is 1. This gives you an answer of y = 1.
Answer:
y = 1
Step-by-step explanation:
Just took the practice test and got it right
The bar graph below shows trends in several economic indicators over the period . Over the six-year period, about what was the highest consumer price index, and when did it occur? Need help with both questions!
Solve the inequality. –10d ≥ –70
Answer:
d≤7
Step-by-step explanation:
-10d≥-70
d≤7
Find the first four terms of the sequence given a1=31 and an+1=an−3
Step-by-step explanation:
Given the formula
a(n+1)=an−3
The first term a(1) = 31
For the second term
a(2)
We have
a( 1 + 1) = a(1) - 3
a(2) = 31 - 3
a(2) = 28
For the third term
a(3)
We have
a(2+1) = a(2) - 3
a(3) = 28 - 3
a(3) = 25
For the fourth term
a(4)
That's
a(3+1) = a(3) - 3
a(4) = 25 - 3
a(4) = 22
Hope this helps you
PLEASE ANSWER FAST PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! The point (1, −1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.
Answer:
sin = -√2 / 2
cos = √2 / 2
tan = -1
Step-by-step explanation:
Θ is in quad IV
sin = -√2 / 2
cos = √2 / 2
tan = -1
7987.1569 to the nearest thousandth
Answer:
7987.1569 to the nearest thousandths is 7987.157
Step-by-step explanation:
What is closest to the area of this section of the garden?
Answer:
117.984ft^2
Step-by-step explanation:
To find the area of a circle the formula is PiR^2 so the area for the full 360 degree circle is. 530.929 ft^2.
Now that we know this we can use a ratio.
530.929/360=x/80
u divide out the left side and multiply it by 80.
so that shows that the area of this circle is
117.984ft^2
Evaluate the expression 23^0-15^1+18^0+(43-12)
Answer:
18
Step-by-step explanation:
23^0 - 15^1 + 18^0 + (43 - 12) =
= 1 - 15 + 1 + 31
= -14 + 1 + 31
= -13 + 31
= 18
here is the picture pls answer another for my lil friend lol
Answer:
Hey there!
The perimeter can be expressed as 140+140+68[tex]\pi[/tex]
This is equal to 493.52 m
Hope this helps :)
20x^3+8x^2-30x-12 Rewrite the expression as the product of two binomials.
Answer:
see below
Step-by-step explanation:
20x^3+8x^2-30x-12
Factor out the greatest common factor 2
2 (10x^3+4x^2-15x-6)
Then factor by grouping
2 ( 10x^3+4x^2 -15x-6)
Factor out 2 x^2 from the first group and -3 from the second group
2 ( 2x^2( 5x+2) -3( 5x+2))
Factor out ( 5x+2)
2 ( 5x+2) (2x^2-3)
The 2 can go in either term to get binomials
( 10x +4) (2x^2-3)
or ( 5x+2) ( 4x^2 -6)
Answer:
[tex](10x+4)(2x^2 -3)[/tex]
Step-by-step explanation:
[tex]20x^3+8x^2-30x-12[/tex]
Rewrite expression (grouping them).
[tex]20x^3-30x+8x^2-12[/tex]
Factor the two groups.
[tex]10x(2x^2 -3)+4(2x^2 -3)[/tex]
Take the common factor from both groups.
[tex](10x+4)(2x^2 -3)[/tex]
The charge to rent a trailer is $2525 for up to 2 hours plus $99 per additional hour or portion of an hour. Find the cost to rent a trailer for 2.82.8 hours, 33 hours, and 8.78.7 hours. Then graph all ordered pairs, (hours, cost), for the function.
The question is not written properly! Complete question along with answer and step by step explanation is provided below.
Question:
The charge to rent a trailer is $25 for up to 2 hours plus $9 per additional hour or portion of an hour.
Find the cost to rent a trailer for 2.8 hours, 3 hours, and 8.7 hours.
Then graph all ordered pairs, (hours, cost), for the function.
Answer:
ordered pair = (2.8, 34)
ordered pair = (3, 34)
ordered pair = (8.7, 88)
Step-by-step explanation:
Charge for 2.8 hours:
$25 for 2 hours
$9 for 0.8 hour
Total = $25 + $9
Total = $34
ordered pair = (2.8, 34)
Charge for 3 hours:
$25 for 2 hours
$9 for 1 hour
Total = $25 + $9
Total = $34
ordered pair = (3, 34)
Charge for 8.7 hours:
$25 for 2 hours
$9 for 1 hour
$9 for 1 hour
$9 for 1 hour
$9 for 1 hour
$9 for 1 hour
$9 for 1 hour
$9 for 0.7 hour
Total = $25 + $9 + $9 + $9 + $9 + $9 + $9 + $9
Total = $88
ordered pair = (8.7, 88)
The obtained ordered pairs are graphed, please refer to the attached graph.
Write an equation and then solve each word problem: My computer can download a movie in 5 hours. If I install an extra processor it can download the movie in 4 hours. How long, working alone, would it have taken the new extra processor to download the movie? Pls help me within 10 minutes
Answer:
The new extra processor would take 20 hours to download the movie.
Step-by-step explanation:
This word problem presents two variables: [tex]n[/tex] - Processing capacity, dimensionless; [tex]t[/tex] - Download time, measured in hours. Both variables exhibit a relationship of inverse proportionality, that is:
[tex]t \propto \frac{1}{n}[/tex]
[tex]t = \frac{k}{n}[/tex]
Where [tex]k[/tex] is the proportionality constant.
Now, let suppose that original processor has a capacity of 1 ([tex]n = 1[/tex]), the proportionality constant is: ([tex]t = 5\,h[/tex])
[tex]k = n\cdot t[/tex]
[tex]k = (1)\cdot (5\,h)[/tex]
[tex]k = 5\,h[/tex]
The equation is [tex]t = \frac{5}{n}[/tex] and if time is reduced to 4 hours by adding an extra processor, the processing capacity associated with this operation is: ([tex]t = 4\,h[/tex])
[tex]n = \frac{5}{t}[/tex]
[tex]n = \frac{5\,h}{4\,h}[/tex]
[tex]n = 1.25[/tex]
Then, the extra processor has a capacity of 0.25. The time required for the new extra processor to download the movie is: ([tex]n = 0.25[/tex])
[tex]t = \frac{5\,h}{0.25}[/tex]
[tex]t = 20\,h[/tex]
The new extra processor would take 20 hours to download the movie.
This table shows values that represent an exponential function.
What is the average rate of change for this function for the interval from x = 1
to x = 3?
Answer:
B. 3
Step-by-step Explanation:
To find the average rate of change of the exponential function represented by the table of values above can be calculated using the general formula for average rate of change of a function, which is given as [tex] m = \frac{f(b) - f(a)}{b - a} [/tex]
Where,
[tex] a = 1, f(1) = 7 [/tex]
[tex] b = 3, f(3) = 13 [/tex]
Plug in the above values in the average rate of change formula:
[tex] m = \frac{13 - 7}{3 - 1} [/tex]
[tex] m = \frac{6}{2} [/tex]
[tex] m = 3 [/tex]
Average rate of change is B. 3
Answer:
3
Step-by-step explanation:
In a sequence, the 40th term is 70, the 41st term is 72 and the 42nd term is 74.
a) State the term-to-term rule
b) Work out the first term
c) Work out the 80th term
Answer:
term to term rule is +2
The first term is -8
80th term is 150
Step-by-step explanation:
70 to 72 is adding 2
72 to 74 is adding 2
term to term rule is +2
The equation for a sequence like this is
xn = a + d(n−1)
where n is the term number a is the first term and d is the term to term rule
Using the 40th term is 70
70 = a + 2( 40-1)
70 = a + 2( 39)
70 = a + 78
Subtract 78 from each side
-8 = a
The first term is -8
80th term
xn = a + d(n−1)
x80 = -8 +2 (80-1)
= -8+2(79)
= -8+158
= 150
need help with this question
Answer:
[tex] - 2 {x}^{5} {y}^{7} [/tex]Last option is correct.
Step-by-step explanation:
[tex] - 2 {x}^{3} {y}^{4} {x}^{2} {y}^{3} [/tex]
Multiply the terms with the same base by adding their exponents
[tex] - 2 {x}^{3 + 2} {y}^{4 + 3} [/tex]
Add the numbers
[tex] - 2 {x}^{5} {y}^{7} [/tex]
Hope this helps..
Best regards!
[tex] - 2 {x}^{5} {y}^{7} [/tex]
Solution:
[tex] - 2 {x}^{3} {y}^{4} {x}^{2} {y}^{3} [/tex]
[tex] = 2 {x}^{(3 + 2)} {y}^{(4 + 3)} [/tex]
[tex] = - 2 {x}^{5} {y}^{7} [/tex]
[tex]{\boxed{\blue{\textsf{Some Important Laws of Indices}}}}[/tex]
[tex]{a}^{n}.{a}^{m}={a}^{(n + m)} [/tex]
[tex]{a}^{-1}=\dfrac{1}{a}[/tex]
[tex]\dfrac{{a}^{n}}{ {a}^{m}}={a}^{(n-m)}[/tex]
[tex]{({a}^{c})}^{b}={a}^{b\times c}={a}^{bc}[/tex]
[tex] {a}^{\frac{1}{x}}=\sqrt[x]{a}[/tex]
[tex]a^0 = 1[/tex]
[tex][\text{Where all variables are real and greater than 0}][/tex]
Write an expression for each statement and then simplify it, if possible.
g
There are two numbers, that sum up to 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers ?
Answer:
If the smaller number is x, then the equation is
. The numbers are
,
.
Answer:
x = 18; y = 35
Step-by-step explanation:
This gives us the equation:
1. x+y=53
2. 3x=y+19
3. 3x-y=19
Add the first and last line together: x+y+3x-y=53+19
Simplifies to: 4x=72
Divide by 4 to get: x = 18
Plug your numbers into the first equation to get 18+y=53; y = 35.
Answer:
The numbers are 18 and 35.
Step-by-step explanation:
The smaller number is x.
Let the other number by y.
Three times the smaller number is equal to 19 more than the larger number.
3x = y + 19
The larger number is
y = 3x - 19
the numbers add up to 53
x + y = 53
x + 3x - 19 = 53
4x = 72
x = 18
y = 3x - 19 = 3(18) - 19 = 54 - 19 = 35
The numbers are 18 and 35.
What is the quotient in polynomial form?
Answer:
Step-by-step explanation:
We are given the polynomial [tex]x^3+2^2-2x+3[/tex] and we are dividing by (x+3). So by performing one step of synthetic division we get
1 2 -2 3|-3
-3 3 -3
1 -1 1 0
So the quotient in polynomial form is [tex]x^2-x+1[/tex]