Answer:
x = 200
Step-by-step explanation:
Given equation:
[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}y=30[/tex]
Steps:
1. Substitute 15 as the value of y in the equation:
[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}(15)=30\ \textsf{[ multiply ]}\\\\\Rightarrow \dfrac{1}{5}x-\dfrac{30}{3}=30\ \textsf{[ simplify ]}\\\\\Rightarrow \dfrac{1}{5}x-10=30[/tex]
2. Add 10 to both sides:
[tex]\sf \dfrac{1}{5}x-10+10=30+10\\\\\Rightarrow \dfrac{1}{5}x=40[/tex]
3. Multiply both sides by 5 to isolate x:
[tex]\sf 5\left(\dfrac{1}{5}\right)x=5(40)\\\\\Rightarrow x=200[/tex]
4. Check your work:
[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}y=30\ \textsf{[ substitute 200 for x, and 15 for y ]}\\\\\dfrac{1}{5}(200)-\dfrac{2}{3}(15)=30\ \textsf{[ multiply ]}\\\\\dfrac{200}{5}-\dfrac{30}{3}=30\ \textsf{[ divide ]}\\\\40-10=30\ \textsf{[ subtract ]}\\\\30=30\ \checkmark[/tex]
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Hey there!
Answer :[tex] \boxed{\bold{\green{ x = 200}}} [/tex]
[tex] \\ [/tex]
Explanation:Given expression :
[tex] \sf{ \frac{1}{5} \green{x} - \frac{2}{3} \orange{y} = 30 } [/tex]
1) Substitue 15 for [tex] \sf{\orange{y}} [/tex] :
[tex] \sf{ \frac{1}{5} \green{x} - \frac{2}{3} \orange{ \times 15} = 30 } \\ \\ \implies\sf{ \frac{1}{5} \green{x} - \frac{30}{3} = 30 } \\ \\ \implies\sf{ \frac{1}{5} \green{x} - 10= 30 } [/tex]
[tex] \\ [/tex]
2) Solve for x :
[tex]\sf{ \frac{1}{5} \green{x} - 10= 30 } [/tex]
⇢Add 10 to both sides of the equation :
[tex]\sf{ \frac{1}{5} \green{x} - 10 \: \bold{+ \: 10}= 30 \: \bold{+ \: 10 }} \\ \\ \implies \sf{\frac{1}{5} \green{x} \: = 40 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
⇢Multiply both sides of the equation by 5:
[tex] \Big( \dfrac{1}{5} \green{x}\Big) \: \bold{ \times \: 5}=40 \: \bold{ \times \: 5} \\ \\ \implies \sf{\dfrac{5}{5} \green{x} \: = 200} \\ \\ \implies \green{ \boxed{\sf{x = 200}}}[/tex]
[tex] \\ [/tex]
3) Let's check our answer by replacing [tex] \green{x} [/tex] with 200 and [tex] \orange{y} [/tex] with 15 :
[tex] \sf{\dfrac{1}{5}\overbrace{\green{\times \: 200}}^{\green{x}} - \dfrac{2}{3}\underbrace{\orange{\times \:15}}_{\orange{y}}= \dfrac{200}{5} - \dfrac{30}{30} = 40 - 10 = \boxed{ 30} } [/tex]
[tex] \\ \\ [/tex]
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Fiona recorded the mean math exam grade for six random samples of students from the entire seventh-grade class. Sample Sample Mean Grade 1 65 2 92 3 78 4 45 5 95 6 70 Why is a valid prediction for the mean of the population not possible using these samples?
The reason why Fiona cannot make a valid prediction based on the mean of the population is that the variation of Fiona’s samples is too large.
Why can't Fiona use the means she recorded?Mean is quite sensitive to outliers so it is best used when the variation between variables is not too much.
In Fiona's case, there variation is quite high with high variable of 95 compared to a low value of 45.
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Answer: just confirming/
Step-by-step explanation:
Whic
the following is an angle? (3 points
Figure A has two rays connected at a vertex, Figure B is a line with one endpoint and the other end has an arrow, Figure C is a line with two endpoints, and Figure D is a line with an arrow at each end
Figure A
Figure B
Figure C
Figure D
Figure A which has two rays connected at a vertex is an angle in this scenario.
What is an Angle?This is formed when two rays share a common endpoint with there being different types of angles.
The common endpoint shared forms a vertex which is why Figure A was chosen as the most appropriate choice.
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Part b
what is the area of the target that earns at least 30 points on a throw?
select the correct from the drop-down menu.
the area is ____ square inches.
a) 16
b) 49
c) 121
d) 144
please help... Find the volume of pyramid that has a square base.
Answer:
V = 324 cm³
Step-by-step explanation:
the volume (V) of the pyramid is calculated as
V = [tex]\frac{1}{3}[/tex] Ah ( A is the area of the base and h the height )
here A = 9² = 81 cm² and h = 12 , then
V = [tex]\frac{1}{3}[/tex] × 81 × 12 = 27 × 12 = 324 cm³
whats equlvlent to 3√6
Answer:
Important: 3
6
looks like a fraction, but it is actually an improper fraction.
There is an infinity number of equivalent fractions to 3
6
.
To find an equivalent fraction to 3
6
, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:
By dividing the original fraction by 3, we get:
3 ÷ 3
6 ÷ 3
= 1
2
By multiplying the original fraction by 2, we get:
3 × 2
6 × 2
= 6
12
Step-by-step explanation:
solve for x. x^2+12x<-11
x²+12x<-11
x²+12x+11<0
x²+12x+11=0
(x+11)(x+1)=0
x+11=0 x+1=0
x= -11 x= -1
Solution: ] -11 , -1 [
Regress smoker on cubic polynomials of age, using a linear probability model. What is the p-value for testing the hypothesis that the probability model is linear in age? (two decimal places)
The statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.
What is probit regression?A probit model is a type of regression in statistics where the dependant variable can only take two values.
We have:
Regress smoker on cubic polynomials of age
If we use linear probability model.
Here the data are missing, but we can say about the estimate that:
Only the estimate intercept is statistically significant at the 5% level is wrong,
Thus, the statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.
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What is the period of f(x) = sin (8x)?
X/8
X/4
4
8
Answer: B- x/4
Step-by-step explanation:
The period is the horizontal distance needed for the values to repeat themselves.
A brick of aluminum weighs 19,745 grams and has the following dimensions: length 29 cm, height 15 cm, and width 51 mm. What is the approximate density of the aluminum? Round to the nearest tenth.
If the volume of the aluminum brick will be 2218.5 cubic cm. Then the approximate density of the aluminum will be 8.9 grams per cubic cm.
What is density?Density is defined as the mass per unit volume. It is an important parameter in order to understand the fluid and its properties. Its unit is kg/m³.
The mass and density relation is given as
Density = mass/volume
A brick of aluminum weighs 19,745 grams and has the following dimensions: length 29 cm, height 15 cm, and width 51 mm.
Then the approximate density of the aluminum will be
The volume of the aluminum brick will be
V = 29 x 15 x 5.1
V = 2218.5 cubic cm
Then the density will be
D = 19,745 / 2218.5
D = 8.900 gram per cubic cm
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If a baseball player hits 10 home runs in the first 45 game, at the same rate how many home runs can he expect to hit during the 162 game season
Using proportions, it is found that he can be expected to hit 36 home runs during the 162 game season.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the player hits 10 home runs in 45 games, hence the proportion is:
p = 10/45.
Then, in 162 games, the amount is:
HR = 10/45 x 162 = 36.
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Over What Interval is The Function In This Graph Increasing?
The correct answer is option D.which is -4 ≤ x ≤ 1.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
in the graph, we can see that the value of x is increasing from -4 coordinate of x to the 1 coordinate of x so the interval will be given as -4 ≤ x ≤ 1.
Therefore the correct answer is option D.which is -4 ≤ x ≤ 1.
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Select all the correct graphs.
Choose the graphs that indicate equations with no solution.
The graphs with no solutions are the ones with no intercepts between the curves. These are the first one and the last one.
Which graphs indicate equations with no solutions?If we have an equation like:
f(x) = g(x).
One way of finding the solutions is to graph:
y = f(x) and y = g(x) and see where the two curves intercept.
From that, the graphs where the curves do not intercept are the graphs that indicate that the equations have no solutions.
The two graphs with no intercepts are the first one (top left) and the last one (bottom right), so these are the correct options.
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Answer:
kid named finger
Step-by-step explanation:
I simply just used a form of alien math solving and I got my answers but I'm not willing to share
Solve the following quadratic equation for all values of x in simplest form.
10-3x²=-2
Answer:
x = ± 2
Step-by-step explanation:
10 - 3x² = - 2 ( subtract 10 from both sides )
- 3x² = - 12 ( divide both sides by - 3 )
x² = 4 ( take square root of both sides )
x = ± [tex]\sqrt{4}[/tex] = ± 2
then x = - 2, x = 2
Answer:
x=2,-2
Step-by-step explanation:
10-3[tex]x^2\\[/tex]=-2
Can also be written as 12=3[tex]x^2[/tex]
[tex](12=3x^2)/3[/tex]
[tex]4=x^2\\\sqrt{4} =+-\sqrt{x^2} \\[/tex]
2=+-x or x=2,-2
x=2,-2
The first term in an arithmetic sequence is -3. If the sequence has a common difference of 8, what is the 30th term in the sequence?
Will give brainliest to right answer :))
Answer:
229
Step-by-step explanation:
(my work for the problem is in the photo I attached)
(I also wrote this step-by-step in the photo because I can explain things better as I do them)
This will be a little bit confusing without me writing out the numbers, so mainly this is if you can't read my handwriting
-3 + 8 = 5 ; 5 + 8 = 13
(1st term) (2nd term) (3rd term)
Instead of adding 8 repeatedly (repeated addition), we can use multiplication.
To get the 3rd term in this sequence, we had to add 8 twice, which could also be done by multiplying 8 twice (8 x 2)
13 + 8 = 21
(4th term)
to get the 4th term, we added 8 three times (or, 8 x 3)
So, if we are looking for the 30th term in a sequence, we will have to add 8, 29 times (8 x 29) to our original term.
8 x 29 = 232
-3 + 232 = 229
This means that the 30th term of the sequence will be 229.
The displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled with the equation d = 0.4 sine (1760 pi t). what is the maximum displacement of the tuning fork?
The maximum displacement of the tuning fork is 0.4 mm
What is a tuning Fork ?A tuning fork is a acoustic resonator , It is used to tune musical Instruments.
It is given in the question that the
displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled with the equation d = 0.4 sine (1760 pi t).
the maximum displacement of the tuning fork = ?
The equation for a sine function is given by
f(t) = A sin(Bt + C) + D
here A is the maximum Displacement
When this equation is compared with the given equation
d = 0.4 sine (1760 pi t).
A = 0.4
The maximum displacement of the tuning fork is 0.4 mm
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What is the slope of the line that passes through the points (-6, 8) and (-9, 7)? Write your answer in simplest form.
Answer:
m=1/3
equation y=1/3x+10
Step-by-step explanation:
Find the rise and run.
1. -6--9=run=3
2. 8-7=rise=1
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the slope of the line that passes through (-6, 8) and (-9, 7).
[tex]\triangle~\fbox{\bf{KEY:}}[/tex] (formula for Slope)
[tex]\longmapsto\bf{\cfrac{y2-y1}{x2-x1}}[/tex]
y2 & y1 = the y-coordinates of the two points
x2 & x1 = the x-coordinates of the two points
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{y2\;and\;y1\;are\;y-coordinates\;of\;the\;two\;points,\;and\;x2\;and\;x1\;are\;x-coordinates}}[/tex]
So we substitute the values and obtain:
[tex]\bf{\cfrac{7-8}{-9-(-6)}[/tex]
Simplifying:
[tex]\bf{\cfrac{-1}{-9+6}}[/tex]
Simplifying more:
[tex]\bf{\cfrac{-1}{-3}}[/tex]
Divide the top and bottom by -1:
[tex]\bf{\cfrac{1}{3}}[/tex]
There's the slope.
Hope it helps you out! :D
Ask in comments if any queries arise.
~Just a smiley person helping fellow students
Alex wants to cover his wall
with a circular clock that has a
diameter of 16 in. How much
space will the clock cover on
his wall?
Answer: A = π r2
r=8 and 8 squared is 64 and 64×3.14=200.96 or rounded to the nearest whole number it would be 201
Step-by-step explanation: brainliest please?
The heights of 150 oak trees are normally
distributed with a mean of 84 feet and a
standard deviation of 3 feet. about how
many trees fall within two standard
deviations of the mean?
Using the Empirical Rule, it is found that about 143 trees fall within two standard deviations of the mean.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.95% of the measures are within 2 standard deviations of the mean, hence, out of 150 trees, the amount is:
A = 0.95 x 150 = 142.5, rounded to 143.
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TRUE OR FALSE
1. Standard units gives a consistent and accurate of the volume of a container.
TRUE OR FALSE ?
Answer:
True
Step-by-step explanation:
Cant really provide step by step per se.
The volume of a rectangular prism is 400 cm3 . If the length is 16 cm and the width is 5cm, what is its height?
Answer:
H = 5
Step-by-step explanation:
rectangular prism:
V = L x W x H
400 cm3 = 16 x 5 x H
400 cm3 = 80 x H
400/80 = 5
h = 5 cm
95% sure this is correct! :)
Answer:
5 cm
Step-by-step explanation:
Formula used :
Volume of the rectangular prism = Length × Width × Height
=========================================================
Given :
⇒ Volume = 400 cm³
⇒ Length = 16 cm
⇒ Width = 5 cm
===========================================================
Solving :
⇒ 400 cm³ = 16 cm × 5 cm × Height
⇒ Height = 400 cm³ / 80 cm²
⇒ Height = 5 cm
Write the expression for the steps "12 increased by 4 and then double it." Then solve.
Solve the following equation for x.
(5/6)x + 10 = 30
x = 24
x = 20
x = 20/6
x = 25/6
Answer:
x=24
Step-by-step explanation:
6×(5/6)x +6(10)=6(30)
5x +60=180
5x +60-60=180 - 60
5x=180 -60
5x=120
5x/5 =120/5
x=24
A school sold all but 5 of ta school sold all but 5 of their old computers for r1200 each the school received r18000 from the sale. how many comps did the school originally old computers for r1200 each the school received r18000 from the sale. how many comps did the school originally have
Answer:
20
Step-by-step explanation:
The proceeds from the sale can be described by an equation involving the original number of computers.
__
setupLet n represent the number of computers the school originally had. Then n-5 is "all but 5" and is the number sold. Each is sold for ₹1200, and the value of the sale is ₹18000. This can be expressed by the equation ...
(n -5)×1200 = 18000
__
solutionThis 2-step linear equation can be solved by dividing by the coefficient, and adding the opposite of the constant.
n -5 = 18000/1200 = 15 . . . . . divide by 1200
n = 15 +5 = 20 . . . . . . . . . . add the opposite of -5
The school originally had 20 computers.
The question is in the picture.
Answer:
x² - 22x + y² + 18y + 58 = 0
Step-by-step explanation:
Using the equation of a circle :
(x - h)² + (y - k)² = r²
Solving :
Substitute 11, -9, 12 in place of h, k and r respectively.
(x - 11)² + (y + 9)² = (12)²x² - 22x + 121 + y² + 18y + 81 = 144x² - 22x + y² + 18y + 202 = 144x² - 22x + y² + 18y + 58 = 0Expand and simplify
(5x + 2)(x + 2)
Answer:
5x²+12x+4
Step-by-step explanation:
5x²+10x+2x+4
5x²+12x+4
Answer:
[tex]5x^{2}+12x+4[/tex]
Step-by-step explanation:
Use the FOIL method to expand.
5x*x+
2*x+
5x*2+
2*2
which is
5x^2+2x+10x+2
combining the two x s we get
5x^2+12x+4
i can figure out
12 is greater than four times a number g
Answer:
"Find g to make this statement true".
12 > 4 • g
The answer of the given expression is 1 & 2.
Concept:Firstly, convert word form into numerical expression.Then Simplify the given expression.How to solve the given question?Convert word form into numerical expression.Thus, the answer of the given expression is 1 & 2.
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STATISTICS in a recent year the mean score on the mathematics section of the SAT test was 515 and the standard deviation was 114. This means that people within one deviation of the mean have SAT math scores that are no more than 114 points higher or 114 points lower than the mean A. write an absolute value inequality to find the range of SAT mathematics test scores within one standard deviation of the mean B. what is the range of SAT mathematics test scores 12 standard deviation from the mean?
An absolute value inequality to find the range of SAT mathematics test scores within one standard deviation of the mean is; |x – 515| ≤ 114
How to Write Inequalities?
A) We are told that;
Mean score = 515
Standard deviation = 114
We are now given that people within one deviation of the mean have SAT math scores that are no more than 114 points higher or 114 points lower than the mean. Thus, the absolute value inequality is;
|x – 515| ≤ 114
B) The range of scores to within ±2 standard deviations of the mean is;
Range = 515 ± 2(114)
Range = 287 to 743
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Based on the data in this two-way table, which statement is true?
Type of Flower/Color Red Pink Yellow Total
Rose 40 20 45 105
Hibiscus 80 40 90 210
Total 120 60 135 315
A.
A flower being pink and a flower being a rose are independent of each other.
B.
A flower being pink is dependent on a flower being a rose.
C.
A flower being a rose is dependent on a flower being pink.
D.
A flower being pink and a flower being a rose are the same.
Tyger buys his car for $6900 he spends some Time repairing it and improving it. He sells it for $9200. What is his percentage profit?
If Tyler sold his car for $9200, then the approximate percentage profit for this product is 33.3%.
How to calculate the percentage?Final price - initial price
$9200 - $6900 = 2300Calculate the percentage $2300 is equivalent to by using the information you already have.
6900 = 1002300 = xx= 100 x 2300/ 6900x= 33.3%33.3% is the profit percentage.
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which of the following equations will produce the graph shown below?
A circle can be characterized by its center's location and its radius' length. The correct option is A.
What is an equation of a circle?A circle can be characterized by its center's location and its radius' length. Let the center of the considered circle be at (h,k) coordinate and the radius of the circle be 'r' units. Then, the equation of that circle would be:
(x-h)² + (y-k)² = r²
The given graph is the graph of a circle that has its origin at (0,0) and has a radius of 4 units, therefore, the equation will be,
(x-0)² + (y-0)² = 4²
x² + y² = 16
Multiply both the sides of the equation by 2,
2x² + 2y² = 32
Hence, the correct option is A.
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