Answer:
B
Step-by-step explanation:
I used substitution to solve this system. I'll run through all of my steps below:
[tex]4x+7y=85\\x=2y-5[/tex]
I'm going to replace the 'x' values in the first equation with the entire second equation.
[tex]4(2y-5)+7y=85[/tex]
[tex]8y-20+7y=85\\15y-20=85\\15y=105\\y=7[/tex]
Now that we know what y equals, we can go back and solve for x.
[tex]x=2(7)-5\\x=14-5\\x=9[/tex]
Hope this helps!
Hurry help me pls
1/2 (6a + 8)=14
Answer:
a= 10/3
Step-by-step explanation:
multiply both sides by 2
get 6a +8 =28
subtract 8 from both sides
you get 6a=20
divide 6 both sides and 10/3.
Determine the two z-scores that divide the area under the standard normal curve into a middle 0.874 area and two outside 0.063 areas.a. -1.45, 1.45
b. -1.39, 1.39
c. -1.53, 1.53
d. -1.46, 1.46
What is the cost of a $40 after a 15% mark-up?
Answer:
Revenue: $46
Profit: $6
Michael went on a hike and recorded his elevation. In total, he went up 14.26 kilometers and went down 11.86 kilometers. His friend Andre did a different hike, and his net elevation gain was 2.5 times Michael’s. What was Andre’s net elevation gain?
Answer:
I don't know
Step-by-step explanation:
LOL XDDDDd
One base of a trapezoid is decreasing at a rate of 888 kilometers per second and the height of the trapezoid is increasing at a rate of 555 kilometers per second. The other base of the trapezoid is fixed at 444 kilometers. At a certain instant, the decreasing base is 121212 kilometers and the height is 222 kilometers. What is the rate of change of the area of the trapezoid at that instant (in square kilometers per second)
The rate of change of the area of the trapezoid at that instant is 5 square kilometers per second and this can be determined by differentiating the area of the trapezoid with respect to time 't'.
Given :
One base of a trapezoid is decreasing at a rate of 8 kilometers per second and the height of the trapezoid is increasing at a rate of 5 kilometers per second. The other base of the trapezoid is fixed at 4 kilometers. At a certain instant, the decreasing base is 12 kilometers and the height is 2 kilometers.First, determine the area of a trapezoid, that is:
[tex]\rm A = \dfrac{b_1+b_2}{2}\times h[/tex]
[tex]\rm \dfrac{2A}{h}=b_1+b_2[/tex]
[tex]\rm b_2 = \dfrac{2A}{h}-b_1[/tex]
Now, differentiate the above expression with respect to 't'.
[tex]\rm \dfrac{db_2}{dt} = -\dfrac{2A}{h^2}\dfrac{dh}{dt}-\dfrac{db_1}{dt}[/tex]
Now. substitute the values of the known terms in the above formula.
[tex]\rm \dfrac{db_2}{dt} = -\dfrac{2\times (16)}{2^2}\times (5)-(-8)[/tex]
[tex]\rm \dfrac{db_2}{dt} = -32\;km/sec[/tex]
So, the area is decreasing at the rate of 5.
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4) Gas mileage is the number of miles you can drive on a a gallon of gasoline.
A test of a new car results in 450 miles on 20 gallons of gas. How far could
you drive on 40 gallons of gas? What is the car's gas mileage?
Answer:
900 miles
Step-by-step explanation:
Simply multiply 450 by 2.
40 ÷ 20 = 2
450 x 2 = 900
OR
Based on Proportion:
[tex]\frac{450}{20}[/tex] x [tex]\frac{x}{40}[/tex]
Cross multiply:
450 x 40 = 18,000
20 x X = 20x
20x = 18,000
Divide by 20:
x = 18,000 ÷ 20
Solve:
x = 900
Tell whether the other pair (8,2) is a solution of the system of linear equations.
x - y = 6
2x - 10y = 4
The ordered pair ______ a solution.
Answers
Is
Is not
The answer is not a solution
By direct evaluation, we will see that the pair (8,2) is not a solution of the system of equations.
Evaluating a system of equations.
A given point is a solution of a system of equations if and only if it is a solution for both equations, then to see if (8, 2) is a solution of the given system, we need to replace the values in both equations and see if it is a solution of each one.
For the first one we have:
x - y = 6
8 - 2 = 6
6 = 6
So (8, 2) is a solution of the first equation.
For the second one we have:
2x - 10y = 4
2*8 - 10*2 = 4
16 - 20 = 4
-4 = 4
Note that this equation is false, then the point (8, 2) is not a solution for the second equation, then the point is not a solution for the system of equations.
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60 POINTS PLEASE HELP! If the parent function f (x) =log (x+1) were replaced by g (x)= -log(x-1) , how would the graph be affected? SEE PHOTO FOR ANSWER OPTIONS
Answer:
C is the correct awnser
Step-by-step explanation:
Randomly selected 150 student cars have ages with a mean of 7.3 years and a standard deviation of 3.6 years, while randomly selected 65 faculty cars have ages with a mean of 5.9 years and a standard deviation of 3.5 years.
1. Use a 0.01 significance level to test the claim that student cars are older than faculty cars.
The test statistic is
Is there sufficient evidence to support the claim that student cars are older than faculty cars?
A. Yes
B. No
2. Construct a 99% confidence interval estimate of the difference μ1−μ2, where μ1 is the mean age of student cars and μ2 is the mean age of faculty cars. <(μ1−μ2)
Answer:
1) B. NO
2) -0.049 < (μ1 − μ2) > 2.751
Step-by-step explanation:
Data of student cars;
Sample size; n1 = 150
Sample mean; x1¯ = 7.3
Sample standard deviation; s1 = 3.6
Faculty cars data;
Sample size; n2 = 65
Sample mean; x2¯ = 5.9
Sample standard deviation; s2 = 3.5
The hypotheses is defined as;
Null hypothesis; H0: μ1 = μ2
Alternative hypothesis; Ha: μ1 > μ2
1) Formula for test statistic for 2 sample test is;
z = (x1¯ - x2¯)/√[((S1)²/n1) + ((S2)²/n2)
z = (7.3 - 5.9)/√[((3.6)²/150) + ((3.5)²/65)
z = 1.4/√((12.96/150) + (12.25/65))
z = 1.4/√0.2749
z = 1.4/0.5243
z = 2.67
From online p-value from z-score calculator attached, using z = 2.67, one tailed test, significance level = 0.01,we have;
P-value = 0.003793
This is less than the significance level, thus we will reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that student cars are older than faculty cars.
2) Formula for the confidence interval is;
CI = μ1−μ2 = (x1¯ - x¯2) ± z√[((S1)²/n1) + ((S2)²/n2)
At significance level of 99%, z-score value is 2.576
Thus;
μ1−μ2 = (7.3 - 5.9) ± 2.576√[((3.6)²/150) + ((3.5)²/65)
μ1 − μ2 = 1.4 ± 2.576(0.5243)
-0.049 < (μ1 − μ2) > 2.751
Given f(x) = - 3x + 1 , solve for a when f(x) = - 5 .
Answer:
x=2
Step-by-step explanation:
-5=-3x+1
-1 -1
-6=-3x
divide both sides by -3
x=2
The value of x when f(x) = - 5, In the function f(x) = - 3x + 1 is 2.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, A function f(x) = - 3x + 1.
Now, when f(x) = - 5 the equation would be,
- 5 = - 3x + 1.
- 5 - 1 = - 3x.
- 6 = - 3x.
3x = 6.
x = 2.
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Consider an ANOVA procedure to compare five population means. In this case, the total number of pairs to be considered in multiple comparisons is ten. If the probability that the null hypothesis is falsely rejected at least once in all six pairs needs to be 0.05, the probability that the null hypothesis is falsely rejected in each pair should be:________. (Give your answer to 4 decimal places.)
Answer:
The right response is "0.0085". A further explanation is given below.
Step-by-step explanation:
Let,
P (across each pair, this same null hypothesis would be wrongly rejected) be "a".
Therefore,
⇒ [tex]P=1-P(no \ time \ rejected)[/tex]
⇒ [tex]1-(1-a)^6 =0.05[/tex]
⇒ [tex]1-a=0.95^{(\frac{1}{6} )}[/tex]
⇒ [tex]a=1-0.95^{(\frac{1}{6} )}[/tex]
⇒ [tex]0.0085[/tex]
Leslie invests $2500 in a savings account for 10 years. The account accrues interest at a rate
of 6% compounded semi-annually. How much money will be in the account at the end of the
10 years?
Answer:
You make $32,000 a year and want to save 10% of your income every year. How much should you put into savings every month?
$32$,000 x 0.10 = 3,200
You want to save $3200 a year.
You should be saving $266.67 a month or $133.33 a paycheck if you are paid
Step-by-step explanation:
Suppose a constellation of stars is plotted on a coordinate plane. The coordinates of one star are (0,-8). The
point representing the star is then translated left 3 units. What are its new coordinates?
1. (0,-5)
2. (-3,-8)
3. (3.-8)
4. (0.-11)
Answer:
4
Step-by-step explanation:
The current of a river is 2 miles per hour. A boat travels to a point 3 miles upstream and back in 2 hours. What is the speed of the boat in still water? The speed of the boat in still water is.
Answer:
1.5 miles per hour
Step-by-step explanation:
3 miles divided by 2 hours
A sporting goods store is having a 15% off sale on all items. Which functions can be used to find the sale price of an
item that has an original price of X? You may choose more than one correct answer.
y=.85 x
Of(x) = 1.15
Sale = Original - 15
Of(x) = x - 15
Sale = Original - 15(Original)
Answer:
The function is:
[tex]f(x) = x - 0.15x[/tex]
Can also be written as:
[tex]Sale = Original - 0.15(Original)[/tex]
Step-by-step explanation:
Given that the sale percentage is 15%
In general, the sale price is calculated by finding the discount according to discount percentage and then subtracting the discount from original price.
Given that x is the original price
Then the discount will be:
[tex]Discount = Original Price * 0.15\\Discount = 0.15x[/tex]
The sale price will be:
[tex]Sale Price = Original\ Price - 0.15(Original\ Price)\\[/tex]
As x is the original price
[tex]f(x) = x - 0.15x[/tex]
Can also be written as:
[tex]Sale = Original - 0.15(Original)[/tex]
An automobile costs $22,750 after a 30% discount. What was the original price of the automobile? (Do not enter the $ sign in your answer.)
Answer:
32,500
Step-by-step explanation:
22,750 = .70x. (Paid 70% since it was 30% discount)
divide both sides by .70
x = 32,500
The table shows how much money a grocery store receives for selling different amounts of asparagus.
ASPARAGUS SALES
NUMBER OF POUNDS
TOTAL SALES
4 lb=
$10
6 lb=
$15
8 lb=
$20
10 lb=
?
12 lb=
?
If the unit rate is constant what are the total sales for 12 pounds of asparagus?
A. $32.50
B. $25.00
C. $22.50
Answer:
The answer is 32.50
Step-by-step explanation:
You would just keep counting up by fives and then you would also have to add tax because it is food -- I am happy to help! :)
Which statement about|-8 is true?
|-8| represents a negative number.
|-8| represents the distance from -8 to 0 on a number line.
|-8|represents the opposite of 8.
|-8| represents the negative distance from 8 to 0 on a number line.
J
Answer:
Your second listed answer choice would be your answer.
Andre is writing a paper for science class. He can type 30 words per minute.
What is the ratio of words to minutes? Write the ratio three ways.
Answer:
30/1, 30:1, 30 to 1
Step-by-step explanation:
Which equation is y = –6x2 + 3x + 2 rewritten in vertex form
Answer:
14 + 3x
Step-by-step explanation:
6x2= 12
12 + 3x + 2
=14 + 3x
Answer:
y =-6(x-1/4)^2+19/8
Step-by-step explanation:
I hope this helps I don't have an explanation I just got it right on EDG 2021
God Bless You!!!!!
Word problem: Jen wants to rent a car. There is a one-time fee of 50 dollars plus 40 dollars per day. Write an algebraic expression for the total cost for “d” days.
A. 90d
B. 50d + 40
C. 50 + 40d
D. 50d + 40d
Please help me!
Answer:
50+40d C
Step-by-step explanation:
A new cream was developed to reduce the irritation caused by poison ivy. To test the effectiveness, researchers put an ad online asking for volunteers to participate in the study. One hundred subjects replied, and they were informed that one group would receive the new cream and the other group would receive a cream with no active ingredient. All 100 subjects were exposed to poison ivy. Fifty were then assigned to the group with the new cream, and 50 were assigned to the group with the cream with no active ingredient. After three days, the subjects’ level of irritation was measured.
Of the 50 subjects that were assigned to the cream with no active ingredient, 15 stated they had less irritation. What is this called?
placebo
control group
placebo effect
placebo control
Answer:
c
Step-by-step explanation:
The effect because of which 15 subjects stated that they had less irritation after having cream with no active ingredient is placebo effect.
What is placebo effect?The placebo effect occurs when a person's physical or mental health appears to improve after receiving a placebo or "dummy" treatment. injections, or even sham surgery.
The placebo effect is caused by an individual's belief in the benefits of the treatment and the expectation that it will make them feel better, rather than by the properties of the placebo.
Given,
50 subjects were assigned to the cream with no active ingredient, 15 stated they had less irritation.
The cream with no active ingredient is placebo, and this effect is called placebo effect.
Hence, 15 subjects stated that they had less irritation is a result of placebo effect.
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Arianna runs up 4 flights of stairs and then runs down 4 flights of stairs.
Does this situation represent additive inverses? Explain.
A
Yes; The numbers combine to eight.
B
Yes; The numbers combine to zero.
No; The numbers are both represented by the same integer.
D
No; The numbers cannot be added together.
Answer:
Yes this represents additive inverse,
Step-by-step explanation:
Since you are subtracting the same number 4 to get to zero.
You deposit $2000 in an account earning 7% interest compounded continuously. How much will you have in
the account in 15 years?
Answer:
$3,715.30
Step-by-step explanation:
Total P+I (A): $3,715.30
Principal (P): $2,000
Compound (n): Continuously
Time (t in years): 15 years
By plugging this into an interest rate calculator, the amount settles to be approximently $3,715.30
Hope this helps!
Complete each congruence. Which is the correspondent side indicated in this picture.
Answer:
Option A
Step-by-step explanation:
Since they are congruent triangles, all the lengths are the same, but it’s just that triangle XYZ is flipped upside down. So if you flip it up to match triangle RTS, then XY is the same as RT.
Hope this helps :)
A cereal box says that now it contains 20% more. Originally, it came with 20 ounces of cereal. How much cereal does the box come with now?
Answer:24ounces
Step-by-step explanation:
Multiply 20 ounces by .20 (The percent) then add your answer to the 20 ounces.
Find the unit rate in decimal representation $150 for 22 ft.²
Answer:
$6.82 per foot
Step-by-step explanation:
To find the unit rate, divide.
150 / 22 ≈ 6.82
Best of Luck!
3. The difference of the squares of two positive consecutive odd integers is 32. Find the
integers.
Answer:
7,9
Step-by-step explanation:
Let two consecutive odd integer=X and (X+1)
The difference of the squares of two positive consecutive odd integers is 32.
So(X+2)^2-x^2=32
(x^2+4+4x)-x^2=32
x^2+4+4x-x^2=32
4x=32-4
4x=28
X=28/4
X=7
So first integer=7
Second integer=7+2
=9.
Fine the distance between (-8, 4) and (-8, -2)
Answer:
The distance between the two points is six units.
Step-by-step explanation:
We are given two coordinate pairs:
(-8, 4)(-8, -2)With these, we can find the distance between the two using the distance formula. The distance formula is:
[tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}, \ \text{where d is the distance.}[/tex]
Additionally, we need to label our coordinates. In math, coordinates are labeled as (x₁, y₁) and (x₂, y₂).
Therefore, our coordinate pairs can be labeled in this format.
(-8, 4)
x₁ = -8y₁ = 4(-8, -2)
x₂ = -8y₂ = -2Now, we can substitute these values into the formula and solve for d.
[tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d = \sqrt{(-8 - -8)^2 + (-2 - 4)^2}\\\\d = \sqrt{(0)^2+(-6)^2}\\\\d = \sqrt{0 + 36}\\\\d = \sqrt{36}\\\\d = 6[/tex]
Therefore, the distance between the two points is six units.
Describe a situation that could be modeled with the ratio 3: 1.
Answer:
three boys to 1 girl
Step-by-step explanation:
a