Answer:
24 cubic inches.
Step-by-step explanation:
[tex]2a \times a^{2} +a^{3} \\2a^{3} +a^{3}[/tex]
[tex]3a^3\\3(2)^3\\3 \times 8[/tex]
An automobile salesman receives a monthly bonus check if his commission income is at least $7,700.00 in a given month. There are 48 automobiles on the lot for sale and he receives a commission of $700.00 per sale. Which inequality shows the number of automobiles,x , the salesman must sell in order for him to receive a bonus check at the end of the month?
Answer:
The inequality that represents the number of cars he needs to sell is: [tex]x \geq 11[/tex]
Step-by-step explanation:
The commission received by the salesman, can be modeled by the following expression:
[tex]\text{commission}(x) = 700*x[/tex]
Where "x" is the number of sold cars. Since he needs to achieve a commission value of at least 7700, then the inequality that represents the number of cars he needs to sell is:
[tex]700*x \geq 7700[/tex]
We can solve for "x" in order to find the number of cars he needs to sell:
[tex]x \geq \frac{7700}{700}\\\\x \geq 11[/tex]
He needs to sell at least 11 cars.
A different breakfast cereal is made using only fruit and bran. The ratio of the weight of fruit to the weight of bran is 1 : 3 (b) What fraction of the weight of this cereal is bran?
Answer:
the answer would be 2/3. I hope this helps.
Step-by-step explanation:
The weight of this cereal is bran is 3/4 fraction.
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given:
A different breakfast cereal is made using only fruit and bran.
The ratio of the weight of fruit to the weight of bran is 1 : 3.
That means,
the total amount = 3x + x = 4x.
Then fraction of the weight of this cereal is bran,
3x/4x
= 3/4
Therefore, 3/4 is the required fraction.
To learn more about the fractions;
https://brainly.com/question/10354322
#SPJ2
Solve the inequality
3(x+1)<9
Answer:
x <2
Step-by-step explanation:
3(x+1)<9
Divide by 3
3/3(x+1)<9/3
x+1 < 3
Subtract 1 from each side
x+1-1 < 3-1
x <2
Answer:
x < 2
Step-by-step explanation:
Distribute the 3 to (x + 1):
3(x + 1)
3x + 3
→3x + 3 < 9
Subtract 3 from both sides:
→3x < 6
Divide both sides by 3:
→x < 2
Robert gets a loan from his bank. He agrees to borrow £6,000 at a fixed annual simple interest rate of 7%. He also agrees to pay the loan back over a 10-year period. How much money in total will he have paid back at the end of the 10 years?
Answer:
The total amount repayable will be £8,280.24.
Step-by-step explanation:
Use the attached formula
Please answer correctly !!!! Will mark brainliest !!!!!!!!!!!!
Answer:
[tex]x^2+10x+24[/tex]
Step-by-step explanation:
So just multiply the sides:
[tex]x^2+6x+4x+24[/tex]
Which is:
[tex]x^2+10x+24[/tex]
I NEED TO HAND IN NOW!!!
PLISSSSS HELP ME ASAP!
Lisa chooses x boys and y girls to join a Mathematics Competition. The total number of pupils chosen is not more than 24 and the number of girls exceeding the number of boys at least by 4
a) Write two linear inequalities
b) Calculate the minimum and maximum number of girls if Lisa chooses 8 boys
Step-by-step explanation:
a)
total no. of pupils is not more than 24
therefore first equation is
(x+y) ≤ 24. ....(1)
No. of girls exceeding the no. of boys by atleast 4
(y-x) ≥ 4. .....(2)
b) Now Liza chooses 8 boys
Maximum no. of girls = ?
Using first inequality
y+8= 24 ( maximum value of less than or equal to function is equal to itself)
Therefore,
y= 24-8
=16
Minimum no. of girls = ?
Using second inequality
y-8 =4 (minimum value of greater than or equal to function is equal to itself)
Therefore,
y= 4+8
y=12
Answer:
a) 2linear inequalities
(x+y) ≤ 24
(y-x) ≥ 4
b) Max no. of girls = 16
Min no. of girls = 12
Hope it helps...
Solve for m.
3>m+8/5
plz helppppp
Answer:
m < 1.4
Step-by-step explanation:
Make [tex]\frac{8}{5}[/tex] a decimal.
1.6
3 > m + 1.6
m < 1.4
Which angle in ADEF has the largest measure?
Answer:
F is the largest angle
Step-by-step explanation:
The largest angle is opposite the largest side. The smallest angle is opposite the smallest side.
The largest side is 4 so the largest angle is F
please solve y = 3x - 1
Step-by-step explanation:
i think question is not complete.
Find the value of a . A.18 B.21 C.20 D.17
Answer:
a =18
Step-by-step explanation:
The two angles are vertical angles and vertical angles are equal
6a +11 = 2a+83
Subtract 2a from each side
6a-2a +11 = 2a-2a+83
4a +11 =83
Subtract 11 from each side
4a +11 -11 = 83-11
4a = 72
divide each side by 4
4a/4 = 72/4
a =18
What is the circumference, in centimeters, of the circle? Use 3.14 for π. Enter your answer in the box.
The diameter is 24.
Please help me, I need this now.
Answer:
75.36 cm
Step-by-step explanation:
Radius for circle is half of diameter
given diameter is 24
therefore radius = half of 24 = 24/2 = 12
circumference of circle is given by [tex]2\pi r[/tex]
where r is the radius
therefore ,circumference of circle
[tex]circumference = 2\pi r = 2*3.14*12\\\\circumference = 75.36[/tex]
Thus, circumference of circle is 75.36 cm
PLS HELP
Simplify the function f(x) =
3x
(81)
4
Then determine the key aspects of the function.
The initial value is
The simplified base is
The domain is
The range is
Answer:
Step-by-step explanation:
This follows the form
[tex]y=a(b)^x[/tex]
where a is the initial value and b is the base with the exponent. Using that information, we can see that the initial value in our function is 1/3. Simplifying the base will take some work. Let's first rewrite this is a radical:
[tex]81^{\frac{3x}{4} }=\sqrt[4]{81^{3x} }[/tex]
Now let's break up 81 into its factors. 81 is 9*9 which is 3*3*3*3. Therefore,
[tex]81=3^4[/tex]
We will use that as a simplification:
[tex]\sqrt[4]{(3^4)^{3x}}[/tex] which simplifies to
[tex]\sqrt[4]{3^{12x}}[/tex]
Rewriting that as an exponent looks like this:
[tex]3^{\frac{12x}{4}}[/tex] which simplifies to
[tex]3^{3x}[/tex]
That's the answer for the second part. The whole exponential equation now is
[tex]f(x)=\frac{1}{3}(3)^{3x}[/tex]
The domain for an exponential function is all real numbers and the range is
y > 0
Answer:
1/3
27
all real numbers
y > 0
ON EDGE
Step-by-step explanation:
PLS HELP!!! WITH MY HOMEWORK
Answer:
$6.8
Step-by-step explanation:
5+10+2+7+10=34
34/5=6.8
The standard deviation of a set of numbers is 22.2. What would the standard deviation be if each one of the numbers in the set was decreased by 4?
Answer:
There would be no change in the standard deviation if each one of the numbers in the set was decreased by 4.
Step-by-step explanation:
We are given that the standard deviation of a set of numbers is 22.2.
And we have to check that what would be the standard deviation, if each one of the numbers in the set was decreased by 4.
For concluding this, we will take a simple example;
Suppose that there are three set of numbers : 6, 8 and 10
Firstly, we will calculate the standard deviation for these numbers;
X [tex]X - \bar X[/tex] [tex](X-\bar X)^{2}[/tex]
6 6 - 8 = -2 4
8 8 - 8 = 0 0
10 10 - 8 = 2 4
8
Here, the Mean of the three numbers is given by;
Mean, [tex]\bar X[/tex] = [tex]\frac{6+8+10}{3}[/tex] = 8
Now, standard deviation formula is given by;
Standard deviation, s = [tex]\sqrt{\frac{(\sum X - \bar X)^{2} }{n-1} }[/tex]
= [tex]\sqrt{\frac{8 }{3-1} }[/tex] = 2
Now, we will decrease each of the three numbers by 4, we get ;
X [tex]X - \bar X[/tex] [tex](X-\bar X)^{2}[/tex]
2 2 - 4 = -2 4
4 4 - 4 = 0 0
6 6 - 4 = 2 4
8
Here, the Mean of the three numbers is given by;
Mean, [tex]\bar X[/tex] = [tex]\frac{2+4+6}{3}[/tex] = 4
Now, standard deviation formula is given by;
Standard deviation, s = [tex]\sqrt{\frac{(\sum X - \bar X)^{2} }{n-1} }[/tex]
= [tex]\sqrt{\frac{8 }{3-1} }[/tex] = 2
From this, we observe that even after decreasing each number by 4, the standard deviation remains same.
SO, we can conclude that if each one of the numbers in the set was decreased by 4 , the standard deviation of a set of numbers will be 22.2 only.
equation of a straight line (see attached)
Answer:
y = 2x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A(4, 7) and (x₂, y₂ ) = B(2,3)
m = [tex]\frac{3-7}{2-4}[/tex] = [tex]\frac{-4}{-2}[/tex] = 2 , thus
y = 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (2, 3), then
3 = 4 + c ⇒ c = 3 - 4 = - 1
y = 2x - 1 ← equation of line
Before graduating this year, a senior homeroom was given a survey. Of those surveyed, 24% felt they learned better at home. Of this group, 80% said they plan on taking an online course in college. Of the students who felt they did not learn better at home, 40% said they plan on taking an online course in college
Part A
What is the probability a person who does not plan on taking an online course felt they learned better at home?
A : 2/21
B : 24/125
C : 38/125
D : 19/31
E :None of these
Part B
What is the probability a person who does plan on taking an online course felt they did not learn better at home?
A : 2/21
B : 24/125
C : 38/125
D : 19/31
E : None of these
Answer:
(A) The correct option is (A).
(B) The correct option is (E).
Step-by-step explanation:
The events can be defined as follows:
X = students felt they learned better at home
Y = students plan on taking an online course in college
The information provided is:
P (X) = 0.24
P (Y|X) = 0.80
P (Y|X') = 0.40
[tex]P(Y'|X)=1-P(Y|X)\\=1-0.80\\=0.20[/tex]
[tex]P(Y'|X')=1-P(Y|X')\\=1-0.40\\=0.60[/tex]
The Bayes' theorem states that the conditional probability of an event E[tex]_{i}[/tex] given that another event A has already occurred is:
[tex]P(E_{i}|A)=\frac{P(A|E_{i})P(E_{i})}{\sum {P(A|E_{i})P(E_{i})}}[/tex]
(A)
Compute the probability a person who does not plan on taking an online course felt they learned better at home as follows:
Use the Bayes' theorem.
[tex]P(X|Y')=\frac{P(Y'|X)P(X)}{P(Y'|X)P(X)+P(Y'|X')P(X')}[/tex]
[tex]=\frac{0.20\times 0.24}{(0.20\times 0.24)+(0.60\times 0.76)}\\\\=0.09524\\\\\approx 0.095[/tex]
Thus, the probability a person who does not plan on taking an online course felt they learned better at home is 0.095 or 2/21.
(B)
Compute the probability a person who does plan on taking an online course felt they did not learn better at home as follows:
[tex]P(X'|Y')=1-P(X|Y')\\=1-0.095\\=0.905[/tex]
Thus, the probability a person who does plan on taking an online course felt they did not learn better at home is 0.905.
The question is in the picture above please help
Answer:
6th degree trinomial
Step-by-step explanation:
Because the highest exponent is 6, and there are 3(tri) numbers.
Answer:
6th degree trinomial.
Highest degree exponent is 6th and three termsRuben and Victor both track the number of miles they walk each day for 6 months. The data is normally distributed for each student.
Ruben had a mean μR of 5 miles with a standard deviation σR=1.1.
Victor had a mean μV of 4.4 miles with a standard deviation σV=1.4.
What are the probabilities that Ruben walked more than 6.1 miles and that Victor walked less than 5.8 miles? Select the probabilities that apply.
16%
34%
68%
545
95%
Answer:
Step-by-step explanation:
Let x be the random variable representing the number of miles that each person walked each day for 6 months. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
For Rueben,
µ = 5
σ = 1.1
the probability that Rueben walked more than 6.1 miles is expressed as
P(x > 6.1) = 1 - P( x ≤ 6.1)
For x = 6.1,
z = (4 - 6.1)/1.1 = - 1.91
Looking at the normal distribution table, the probability corresponding to the z score is 0.02807
P(x > 6.1) = 1 - 0.02807 = 0.97193
P(x > 6.1) = 0.97 × 100 = 97%
For Victor,
µ = 4.4
σ = 1.4
the probability that Victor walked less than 5.8 miless is expressed as
P(x < 5.8)
For x = 5.8,
z = (5.8 - 4.4)/1.4 = 1
Looking at the normal distribution table, the probability corresponding to the z score is 0.8413
P(x < 5.8) = 0.84 = 84%
Which of the following statements is true about an image after a dilation?
Answer:
Not sure what the answer choices are, but choose the choice that says the new image is either stretched or shrunk. In a dilation, the shape/corresponding sides of the pre-image are preserved in the new image, but the size of the new image is altered.
Step-by-step explanation:
hope this helps!
A line with a slope of -2 crosses the y-axis at (0, 3). The equation of the line is ____
Answer:
y=-2x+3
Step-by-step explanation:
equation for slope is y=mx+b
the slope is -2 so that equals m
(0,3) is the y-intercept
y=b
3 is the y value making it substitute b making the equation y=-2x+3
One serving of a cereal is 3/4 cup. Each box of cereal has about 9 cups of cereal and costs $3.80. Is the price per serving greater than $0.50? Complete the explanation.
Answer:
The price per serving is $0.315, therefore, it's less than $0.5
Step-by-step explanation:
In order to calculate the price per serving, we can first calculate the price per cup, this is done by dividing the total value of the box by the number of cups it can serve:
[tex]price_{cup} = \frac{3.8}{9} = 0.42[/tex]
Since each serving is [tex]\frac{3}{4}[/tex] of a cup, then it's price has the same proportion and is given by:
[tex]price_{serving} = \frac{3}{4}*0.42 = 0.315[/tex]
The price per serving is $0.315, therefore, it's less than $0.5
Please help! Correct answer only, please! I need to finish this assgnment this week! Matrix P has a dimensions of 3 X 4 and Matrix Q has the dimensions 4 X 5. Determine the dimensions of the matrix PQ if it is possible. Explain why if it is not. (refer to video part 4) Group of answer choices A. Matrix PQ would have the dimensions 3 X 4 B. Matrix PQ would have the dimensions 4 X 5 C. Matrix PQ would have the dimensions 3 X 5 D. These matrices can not be multiplied because their dimension don't align.
Answer: C
Step-by-step explanation:
Your answer is correct! When you multiply 2 matrices, the inner dimensions have to be equal. If they are equal, the resulting dimensions would be the outer dimentions.
(3×4)(4×5)
Since the inner (bolded) dimensions are the same, in this case 4×4, we know these matrices can be multiplied.
Since these matrices can be multiplied, the product will be 3×5, the underlined outer dimensions.
Find the sum of 6(1-a^2), -2(3-a+2a^2) and 5(-2a+3a^2)
Answer:
[tex]5a^2-8a[/tex]
Step-by-step explanation:
[tex]6(1-a^2)-2(3-a+2a^2)+5(-2a+3a^2)[/tex]
[tex](6)(1)+(6)(-a^2)+(-2)(3)+(-2)(-a)+(-2)(2a^2)+(5)(-2a)+(5)(3a^2)[/tex]
[tex]6+-6a^2+-6+2a+-4a^2+-10a+15a^2[/tex]
[tex](-6a^2+-4a^2+15a^2)+(2a+-10a)+(6+-6)[/tex]
[tex]5a^2-8a[/tex]
If 4 1/2 = 2, 8 1/1= 2, and 16 then for what value of xwould x 1/5 = 2?
24
32
02
04
Answer:
D) 0.0004
Step-by-step explanation:
(0.02)^2=0.02*0.02=0.0004
k (t) = 10t - 19
k(-7) =
Answer:
k(-7) = - 89
Step-by-step explanation:
k (t) = 10t - 19
Let t = -7
k(-7) =10 * -7 - 19
=-70-19
-89
Answer:
[tex]k (-7) = -89[/tex]
Step-by-step explanation:
[tex]k (t) = 10t - 19[/tex]
[tex]k (-7) = 10(-7) - 19[/tex]
[tex]k (-7) = -70 - 19[/tex]
[tex]k (-7) = -89[/tex]
12. What is the measure of an angle if it is nine times
its own
supplement?
Angle
degrees
Answer:
if it's the right angle and it nine times it own
I think it would be 180 degress
Please help me!!!!!!
Answer:
C
Step-by-step explanation:
The addition of the x^5 term makes it non proportional
Answer:
C.
Step-by-step explanation:
A. y = (6x + 3) - 3= 6x
B. y = - 15x
D. = - 1/3 x
All of these are proportional because they have general formula y = kx.
WILL GIVE BRAINLIEST
Answer:
D
Step-by-step explanation:
Since the interior angles of a triangle will always add up to 180 degrees, angle B must equal 180-67-40=73 degrees, meaning that angle B corresponds to angle E in the other triangle. A corresponds to D, and F maps to C. Since no rotation is necessary, all you need to do is align two of the vertices to their corresponding vertice on the other triangle. The only answer choice here that does this is choice D, meaning that it is the correct answer. Hope this helps!
Help please answer quick
Answer:
A) 5
Step-by-step explanation:
Distance between two points is calculated as:
Step 1: locate the coordinate points:
Point 1- (x₁ , y₂) = (-5, -2)
Point 2-(x₁ , y₂)= (-9, -5)
Formula to find distance between two points = √(x₂−x₁)² + (y₂−y₁)²
Step 2: input the values
√(−9− −5)² + (−5− −2)²
= √(−4)² + (−3)²
=√16 + 9
= √25 ........ square root of 25
= 5
Distance between points (-5, -2) and (-9, -5) is 5
work by Tolaosunrinde
Solve for b.
–2.5b + 15.2 = –3.5b
b =
Answer:
Step-by-step explanation:
-2.5b + 15.2 = -3.5b
-2.5b + 2.5b + 15.2 = -3.5b + 2.5b
15.2 = -1b
15.2/-1 = -1b/-1
-15.2 = b
b = -15.2