Answer:
Third option
Step-by-step explanation:
Given the following question:
[tex]7x-4=5x+15[/tex]
To find the answer we need to use inverse of operations to simplify the equation in till we isolate the variable and find the value of x.
[tex]7x-4=5x+15[/tex]
[tex]-4+4=0[/tex]
[tex]15+4=19[/tex]
[tex]7x=5x+19[/tex]
[tex]5x-5x=0[/tex]
[tex]7x-5x=2x[/tex]
[tex]2x=19[/tex]
[tex]2x\div2=x[/tex]
[tex]19\div2=\frac{19}{2}[/tex]
[tex]=\frac{19}{2}[/tex]
Your answer is the third option or "19/2."
Hope this helps.
The human resources manager at a company records the length, in hours, of one shift at work, X. He creates the probability distribution below. What is the probability that a worker chosen at random works at least 8 hours? A probability distribution has the number of hours on the x-axis and the probability on the y-axis. The probability of 6 hours is 0. 02; 7 hours is 0. 11; 8 hours is 0. 61; 9 hours is 0. 15; 10 hours is 0. 9. 0. 62 0. 78 0. 84 0. 96.
The probability that a worker chosen at random works at least 8 hours is Option C: 0.84 approx.
How to evaluate the probability of a random variable getting at least some fixed value?Suppose the random variable in consideration be X, and it is discrete.
Then, the probability of X attaining at least 'a' is written as:
[tex]P(X \geq a)[/tex]
It is evaluated as:
[tex]P(X \geq a) = \sum_{\forall \: x_i \geq a} P(X = x_i)[/tex]
The probability distribution of X is:
x f(x) = P(X = x)
6 0.02
7 0.11
8 0.61
9 0.15
10 0.09
Worker working at least 8 hours means X attaining at least 8 as its values.
Thus, probability of a worker chosen at random working 8 hours is
P(X ≥ 8) = P(X = 8) + P(X = 9) +P(X = 10) = 0.85 ≈ 0.84 approx.
By the way, this probability distribution seems incorrect because sum of probabilities doesn't equal to 1.
The probability that a worker chosen at random works at least 8 hours is Option C: 0.84 approx.
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find the x-intercept of the following linear equation -2x + 3y = 12
Answer:
X = 6
Step-by-step explanation:
Hope this helped!!
maybe mark brainiest
consider the equation 21= m +14 1/6 which which step will help to solve this equation
Answer:
m = 41/6
Step-by-step explanation:
21 = m + 14 1/6Convert everything into improper fractions with a denominator of 6.
21 = m + 14 1/6126/6 = 6m/6 + 85/6126 = 6m + 856m = 126 - 856m = 41m = 41/6-2x + 1 = 4x + 9
I don’t know what to solve for x?
Answer:
x = -1.33333333333
Step-by-step explanation:
[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}[/tex]
[tex]-2x+1-1=4x+9-1[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]-2x=4x+8[/tex]
[tex]\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}[/tex]
[tex]-2x-4x=4x+8-4x[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]-6x=8[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-6[/tex]
[tex]\frac{-6x}{-6}=\frac{8}{-6}[/tex]
[tex]x=-\frac{4}{3}[/tex]
[tex]x=-1.33333333333[/tex]
~Lenvy~
Please help math in the sreenshot
Answer:
yeh
Step-by-step explanation:
1 gallons = 4 quarts
4,8,20,28
quarts= 2 pints
1,3,6,16
1 pint= 2 cups
2,6,5,18
Help anyone?Can u be specific and tell how u got it
Answer:
6 1/4
Step-by-step explanation:
3+2=5
2+3
1/2+3/4= ----------------------------------------------------
4
=5/4
=1 1/4
5+ 1 1/4
=6 1/4
I would just like to know what this means and how to do it consistently. Thanks (:
Answer:
This question is asking for you to determine if the tables represent linear functions, functions in y=mx+b form, and to find the equation for the line.
If something is a linear function, each of the input values will have it's own corresponding y value, therefore c cannot be linear, as -1 and 1 both have 10 as the output.
I hope this helps, but if you need more clarification, please tell me in the comments!
The table shows the sales receipt for your purchase.
a) the items with a "t" next to the price are subject to sales tax. what percent sales tax did you pay?
b) calculate the price of the top.
c) the price you paid for the top was 60% of the original price. what was the original price of the top?
The sales receipt for the purchase includes the sales tax
The sales tax is 6%The price at the top is $7.50The original price at the top is $12.50How to determine the percent of sales tax?The sales tax is calculated as:
Percentage sales tax * (Sum of Items subjected to tax) = Sales tax.
So, we have:
T * (3 + 0.5) = 0.21
Evaluate the sum
T * (3.5) = 0.21
Divide both sides by 3.5
T = 6%
Hence, the sales tax is 6%
The price at the topThe price (p) at the top is calculated using:
p = 13 - 3 - 2 - 0.5
Evaluate the difference
p = 7.5
Hence, the price at the top is $7.50
The original price at the top60% of the original price (P) is p.
So, we have:
60% * P = p
Substitute 7.5 for p
60% * P = 7.5
Divide both sides by 60%
P = 12.5
Hence, the original price at the top is $12.50
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Someone help me with this pls
Answer:
MAYBE
Step-by-step explanation:
Answer:
SORRY
Step-by-step explanation:
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SORRY
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ANSWER
SOORY
evaluate 8-m/n+ p2 when m=8 n=2 p=7
====================================================
let's evaluate this expression
[tex]\pmb{\displaystyle\frac{8-m}{n+p^2} }[/tex]
[tex]\pmb{\displaystyle\frac{8-8}{2+7^2}}[/tex] (step 1)
[tex]\pmb{\displaystyle\frac{0}{2+49}}[/tex] (step 2)
simplify:
[tex]\pmb{\displaystyle\frac{0}{51}}[/tex] (step 3)
[tex]\pmb{0}[/tex] (step 4)
=======================================
note:-Hope everything is clear; if you need any more clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)
Consider the system and find the eigenvalues and the eigenvectors
Eigenvalues are the special set of scalar values which is associated with the set of linear equations in matrix equations.
What are Eigenvalues?
Your information is incomplete. Therefore, an overview will be given. An eigenvector of a linear transformation is a nonzero vector that changes by a scalar factor when the linear transformation is applied to it.
The eigenvectors of matrix A are those vectors X for which multiplication by A will result in a vector in thesame direction or opposite direction to X.
Since the zero vector 0 has no direction, 0 is never allowed to be an eigenvector.
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An eigenvector of a linear transformation and eigenvectors of a system
Ax = Bx can be determined where B is an eigenvalue of A.
What are Eigenvalues?An eigenvector of a linear transformation is a nonzero vector that changes by a scalar factor when the linear transformation is applied to it.
The eigenvectors of matrix A are those vectors X for which multiplication by A will result in a vector in the same direction or opposite direction to X.
The basic equation is
Ax = Bx
here B is an eigenvalue of A.
Since the zero vector has no direction, zero is never allowed to be an eigenvector.
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#SPJ4
Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y)(x,y) point. y=−x ^2 −8
Answer:
Step-by-step explanation:
emma really smells bad do not answer this question
What is the area and circumference of the circle? diameter = 12 cm
Answer:
Circumference = 7.68 cm
Area = 113.04 cm²
Step-by-step explanation:
First, let us find the radius of the given circle.
d = 2r
r = d / 2
r = 12 / 2
r = 6 cm
And now, let us find the circumference of the circle using the below formula.
C = 2 π r
C = 2 × 3.14 × 6
C = 37.68 cm
And now let us find the area of the circle using the below formula.
A = π r²
A = 3.14 × 6 × 6
A = 113.04 cm²
solve for the x in the triangle .
A rectangle has a width that is 5 feet less than the length. The area of the rectangle is 126 square feet. Find the dimensions of the rectangle
Given:
A rectangle has a width that is 5 feet less than the length. The area of the rectangle is 126 square feet[tex]\\[/tex]
❍Let's assume, Length of rectangle x feet and width of the rectangle x - 5 feet respectively.
[tex]\\[/tex]
To calculate the dimensions of the rectangle we will use the formula of Area of rectangle:
[tex]\\[/tex]
[tex] \: \: \: \: \: \: \: { \underline{ \boxed{ \pmb{ \frak{ Area_{(rectangle)} = Length \times width }}}}} \\ \\ [/tex]
[tex]\\[/tex]
[tex] \underline {\sf{Substituting \: the \: values~ in~ above~formula: }} \\ [/tex]
[tex]\\[/tex]
[tex] : \implies \sf \:x \times (x - 5) = 126 \\ \\ \\ : \implies \sf \:x^2 - 5x = 126 \\ \\ \\ : \implies \sf \:x^2 - 5x - 126 = 0 \\ \\ \\ : \implies \sf \:x^2 - 14x - 9x - 126 = 0 \\ \\ \\ : \implies \sf \:x (x - 14) - 9 (x + 14) = 0 \\ \\ \\ : \implies \sf \:(x - 14)(x - 9) = 0 \\ \\ \\ : \implies { \boxed { \purple{\pmb { \: x = 14 \: \: or \: \: x = -9}}} } \\ \\ \\ [/tex]
We know that side can't be negative. So, x = 14 feetHence,
Width of rectangle = x - 5 = 9 feetLength of rectangle = x = 14 feet[tex]\\[/tex]
[tex] \\ { \underline{ \pmb{ \frak{\therefore Dimensions \: of \: rectangle \: are \: 9~ feet \: and \: 14 ~feet \: }}}}[/tex]
Given that, width of the rectangle is 5 feet less than the length and area of the rectangle is 126 sq. feet, and we are told to find the dimensions i.e the length and width of the rectangle.
As we know that the area of a rectangle is length times it's width, so if we assume our length to be x, so our width is just going to be (x - 5) , and putting it in the area formule we can thus obtain;
[tex]{:\implies \quad \sf x(x-5)=126}[/tex]
[tex]{:\implies \quad \sf x^{2}-5x-126=0}[/tex]
[tex]{:\implies \quad \sf x^{2}-14x+9x-126=0}[/tex]
[tex]{:\implies \quad \sf x(x-14)+9(x-14)=0}[/tex]
[tex]{:\implies \quad \sf (x-14)(x+9)=0}[/tex]
So, here either (x - 14) = 0 or (x + 9) = 0, when you equate both, you will get x = 14 or -9 but as x ≠ -9, so x = 14, and then x - 5 = 14 - 5 = 9
Hence, the required length and width are 14 feet and 9 feet respectively
Find the area of the shaded sector of the circle. Give the exact answer in terms of straight pi.
A circle has a central angle that measures 120 degrees and a radius of 8.
fraction numerator 48 straight pi over denominator 9 end fraction units squared
fraction numerator 64 straight pi over denominator 3 end fraction units squared
fraction numerator 32 straight pi over denominator 3 end fraction units squared
fraction numerator 16 straight pi over denominator 9 end fraction units squared
The area of the sector that has a central angle of 120 degrees and radius of 8 units is 64π / 3 units²
Area of a sectorThe area of a sector is defined as follows:
area = ∅ / 360 × πr²
where
r = radius∅ = central angleTherefore,
r = 8
∅ = 120°
Hence,
area of the sector = 120 / 360 × π × 8²
area of the sector = 1 / 3 × π × 64
area of the sector = 64π / 3 units²
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Use the information given to answer the question.
which two inequalities represent the constraints for the art studio classes
per week?
an art studio offers classes for painting and pottery. each painting class is 1
2+ y = 40
hour long. each pottery class is 1.5 hours long. the art studio is only open
0 2 +1.5y = 40
for classes a maximum of 40 hours per week, and only one class is offered at
o +1.5y > 40
35(2 + y) < 1,000
a time. each class costs $35,and the art studio earns a minimum of $1,000
35(x + y) > 1,000
per week from all classes. let be the number of painting classes offered per
calculator
week, and let y be the number of pottery classes offered per week.
The two inequalities that represents the constraints for the art studio classes per week are:
x + 1.5y = 40
35(x + y) > 1,000
What two inequalities represent the constraints?Here are inequalities signs and what they mean:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
= means equal to
The inequality that represents the total hoursthe art studio is open would be an equal to sign. This is because the store is open for a maximum of 40 hours.
The inequality that represents the total earnings would be represented with a greater than sign because the studio earns more than $1000 weekly.
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Line n goes through points A and B. What is the slope of line n?
Point A;(4,7)
Point B:(18,17)
Answer:
The slope is 5/7.
Step-by-step explanation:
Use a slope formula.
Slope:
[tex]\sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]
y₂ = (17)
y₁ = (7)
x₂ = (18)
x₁ = (4)
Rewrite the problem down.
[tex]\sf{\dfrac{17-7}{18-4}=\dfrac{10}{14}={\dfrac{10\div2}{14\div2}=\boxed{\sf{\dfrac{5}{7}}}[/tex]
Therefore, the slope is 5/7.
I hope this helps! Let me know if my answer is wrong or not.
Answer:
5/7
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(17-7)/(18-4)
m=10/14
simplify
m=5/7
-4=7t/5 +4t/5 solve for t
Answer:
t=-\frac{20}{11}
Step-by-step explanation:
Which problem solving strategy would be best to solve this problem?
Your friend's house is 12 miles from your home. Your school is one-third the way from your friend's house and your home. The park is one-fourth the way from the school to your friend's house. How far is the park from your home?
A. guess, check and revise
B. write an equation
C. make a table, chart or list
D. make a model or diagram
The scale factor of a figure and its enlargement is 4. what is the new length of the enlarged figure if the original length is 4.5 cm? 4.0 cm 8.5 cm 16 cm 18 cm
The new length of the enlarged figure will 18 cm.
What is scale factor?A scale factor is a number which scales, or multiplies, the original figure by some quantity.
We have the equation for the scale factor.
Y=Cx
C is a scale factor for x. It is called the constant of proportionality or scale factor of y to x.
As the given length is 4.5 cm, so with a scale factor of 4, the length of the enlarged figure will be
[tex]Y=4.5\times4=18\ cm[/tex]
Therefore, the new length of the enlarged figure will 18 cm.
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Which expression is the factorization of x2 10x 21?
The factorization of the given expression [tex]\rm x^2+10x+21[/tex] is (x+3)(x+7) the option first is correct.
It is given that the expression [tex]\rm x^2+10x+21[/tex]
It is required to find which expression is the factorization of the given expression, the options are:
a) (x + 3)(x + 7)
b) (x + 4)(x + 6)
c) (x + 6)(x + 15)
d) (x + 7)(x + 14)
What is polynomial?Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.
We have an expression:
[tex]\rm x^2+10x+21[/tex]
[tex]\rm x^2+7x+3x+21[/tex]
Breaking 10x into 7x and 3x because the multiplication of 7x and 3x is [tex]\rm 21x^2[/tex] and the addition is 10x.
[tex]\rm x^2+7x+3x+21\\\\\rm x(x+7)+3(x+7)\\\\\rm (x+7)(x+3)[/tex]or
[tex]\rm (x+3)(x+7)[/tex]
Thus, the factorization of the given expression [tex]\rm x^2+10x+21[/tex] is (x+3)(x+7) the option first is correct.
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There are a total of 21 marbles in the box. And 5 of the marbles
are black and 6 of them are blue. A single marble is chosen at
random from the box. What is the probability of choosing a
black ball or a blue ball?
Step-by-step explanation:
there are in total 21 marbles.
5 black, 6 blue = 11 black or blue marbles.
so, the probability of pulling a black or blue marbles is as always desired possible outcomes / total possible outcomes = 11/21
Express in the form n : 1. Give n as a fully simplified fraction. 10 : 12
Answer:
[tex]\frac{5}{6}:1[/tex]
Step-by-step explanation:
[tex]10:12[/tex] divide both sides of this ratio by 12 to give a ratio in the form [tex]n:1[/tex]
[tex]\frac{10}{12}:1[/tex] which simplifies to [tex]\frac{5}{6}:1[/tex]
Question 9 of 12
What is cos 60°?
A. 13
B. 1
C.
2
D.
2.
E.
NS-
F. V
Answer:
D
Step-by-step explanation:
You can find the answer by memorizing the values of the unit circle.
A bedroom door in the house has the same
dimensions as the front door, but the length is
30 inches rather than 36 inches. How much greater is
the volume of the front door than the bedroom door?
The difference in the volume of bedroom door in the house taken the length and width into consideration will be 120 inches³.
How to calculate the bedroom door?It should be noted that the volume of a door is simply gotten by multiplying the length by width.
Let's assume that the width is 20 inches. Therefore, the difference will be:
= (36 × 20) - (30 × 20)
= 720 - 600
= 120 inches³
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The speed of the jet Alyssa flew on from Boston to London was 480 mph. on her return flight, the speed of the jet was 600mph with a tail wind. What was Alyssa's average speed on the round trip?
Based on the speed Alyssa used to get to London and the speed back to Boston, the average speed was 540 mph.
What is the average speed?The average speed that Alyssa was going can be found by the formula:
= (Initial speed + Final speed) / 2
Solving gives:
= (480 + 600) / 2
= 1,080 / 2
= 540 mph
In conclusion, Alyssa's average speed was 540 mph.
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which fraction is between 2/3 and 6/7
Answer:
For example, 16/21
Step-by-step explanation:
Are there choices?
There is an infinite number of numbers between any two numbers.
2/3 = 14/21
6/7 = 18/21
One example of a fraction between 2/3 and 6/7 is 16/21
16/21 is between 2/3 and 6/7.
Liam buys three identical plastic
containers that are right rectangular
prisms. one face of each container
measures 4 and 1/2 in. by 2 in. the total
volume of the three containers is
135 in.. how many of these containers
can liam set on a shelf that is 24 in. long
with the 4and 1/2in-by-2 in. faces touching?
The number of rectangular prism container that would be set on the shelf is: 4.
What is the Volume of a Rectangular Prism?Volume of rectangular prism = length × width ×height
Given the following:
Volume of three containers = 135 in.³Volume of each rectangular prism container = 135/3 = 45 in.³One face = width × height = 4.5 × 2 = 9 in.Find the length of one rectangular prism using the volume formula since volume for one prism = 45 in.³
45 = length × 9
length = 5 in.
Each rectangular prism container is 5 in. long, therefore, the number of the containers that can be set on the shelf that is 24 in. long, if the 4.5 in by 2 in. face touches each other = 24/5 = 4.8.
The fifth container won't fit in. Therefore, the number of rectangular prism container that would be set on the shelf is: 4.
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help on this please.