Answer:
700 miles driven in a day
Step-by-step explanation:
Create an equation to represent the situation, where x is the number of miles.
0.8x + 120 = 0.9x + 50
Solve for x:
120 = 0.1x + 50
70 = 0.1x
700 = x
So, the rental costs will be the same at 700 miles driven in a day.
Determine whether (a) x = -1 or (b) x = 2 is a solution to this equation
Answer:
x = 2 is the solution to x + 1.5 = 3.5
Step-by-step explanation:
x + 1.5 = 3.5
-1.5 -1.5
--------------------
x = 2
1. Find the volume of a rectangular block 15 cm long, 5 cm wide and 10 cm length
9514 1404 393
Answer:
750 cm³
Step-by-step explanation:
The volume is given by the formula ...
V = LWH . . . . where L, W, H represent length, width, height
The volume is the product of the dimensions.
V = (15 cm)(5 cm)(10 cm) = 750 cm³
Charla has six segments with which to make two triangles. The segments lengths are 2 in., 3 in., 4 in., 5 in., 6 in., and 7 in. Which are possible side lengths of her two triangles?
2 in., 4 in., 6 in. and 3 in., 5 in., 7 in.
2 in., 5 in., 6 in. and 3 in., 4 in., 7 in.
2 in., 3 in., 4 in. and 5 in., 6 in., 7 in.
2 in., 3 in., 6 in. and 4 in., 5 in., 7 in.
Answer:
The answer is option C
2 in., 3 in., 4 in. and 5 in., 6 in., 7 in.
Step-by-step explanation:
The scores of a high school entrance exam are approximately normally distributed with a given mean Mu = 82.4 and standard deviation Sigma = 3.3. What percentage of the scores are between 75.8 and 89?
Notice that
75.8 = 82.4 - 6.6 = 82.4 - 2 × 3.3
89 = 82.4 + 6.6 = 82.4 + 2 × 3.3
Then the percentage of students with scores between 75.8 and 89 make up the part of the distribution that lies within 2 standard deviations of the mean. The empirical (68-95-99.7) rule says that approximately 95% of any distribution lies within this range.
Answer:
b
Step-by-step explanation:
A math professor is wondering if students today are better or worse than in the past. He has given the same final to this year's class that he gave ten years ago. Compute mean, median, and mode for both classes and write a paragraph summarizing the differences.
This Year
35 45 65 75 87
80 69 71 53 90
99 95 70 82 73
93 67 61 57 74
72 77 71 81 83
Ten Years Ago
56 77 75 76 59
74 51 89 55 79
67 77 69 91 68
90 65 79 69 79
87 86 98 91 95
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following data:
This year :
35, 45, 53, 57, 61, 65, 67, 69, 70, 71, 71, 72, 73, 74, 75, 77, 80, 81, 82, 83, 87, 90, 93, 95, 99
Mean = ΣX / n = 1825 / 25 = 73
The mode = 71 ( most frequently occurring)
Median = 1/2(n+1)th term = 1/(26) = 13th term
Median = 73
10 years ago :
51, 55, 56, 59, 65, 67, 68, 69, 69, 74, 75, 76, 77, 77, 79, 79, 79, 86, 87, 89, 90, 91, 91, 95, 98
Mean = ΣX / n = 1902 / 25 = 76.08
The mode = 79 ( most frequently occurring)
Median = 1/2(n+1)th term = 1/(26) = 13th term
Median = 77
According to the computed statistics, we can conclude that, today is worse than the past as the average score which is almost similar to the median value is higher 10 years ago and the modal score is better 10 years ago as well.
Last year, Rob set up the Road Runner Race for his school.
The race was 1,200 meters long and 188 people signed up to
run the race. 38 people did not show up to run. This year,
there will be 3 times as many runners as last year. How
many people will run the race this year?
Answer:
450 runners
Step-by-step explanation:
Cheyenne's bi-weekly gross pay is $529.81. She sees that $18.54 was deducted for Medicare tax. What percent of Cheyenne's gross pay has been withheld for Medicare tax? Round to the nearest tenth. (2 points)
0.35%
2.2%
3.5%
Answer:
I got 3.5%
Step-by-step explanation:
Hope this helps
A pizza parlor has a choice of 10 toppings for its pizzas. From these 10 toppings, how many different 7-topping pizzas are possible?
Answer:
120
Step-by-step explanation:
There are 10 possible toppings to choose from, you choose 7.
Using combinatorics, it's 10!/(7! 3!), or 120.
The formula is (total amount to choose from )! divided by (amount you choose)!(amount you don't choose)!
Or search up combination formula
A combination is an arrangement of a set of numbers from a total set where the order of the set is not relevant.
The formula for combination.
= [tex]^nC_r[/tex]
= n! / r! (n -r)!
The number of possible 7-toppings for the pizza is 120.
What is a combination?A combination is an arrangement of a set of numbers from a total set where the order of the set is not relevant.
We have,
The total number of toppings = 10.
n = 10
The number of required toppings = 7.
r = 7
The formula for combination.
= [tex]^nC_r[/tex]
= n! / r! (n -r)!
The possible number of possible 7-toppings pizzas.
= [tex]^{10}C_7[/tex]
= (10 x 9 x 8) / (3 x 2)
= 120
Thus,
n = 10 and r = 7
[tex]^{10}C_7[/tex] = 120
The number of possible 7-toppings for the pizza is 120.
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N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to
N?
A) 1 1/2
B 1 1/3
C) 5/3
D) 3/2
Answer:
it should be letter c 5/3 I could be wrong but I hope this help
properties of exponents. the answer is 1/2^3 i need help with the work
(2^-1)^2/2×2^0
2^(-1×2)/2^1
2^-2/2^1
2^(-2-1)
2^(-3)
(1/2)^3
Properties used (m^n)^a = m^na
(m)^-n = (1/m)^n
m^0 = 1
m^n/m^a = m^(n-a)
Must click thanks and mark brainliest
A researcher wants to better understand the health benefits of eating vegetables. In a study he finds 300 adults aged 45-60 who eat at least 3 servings of vegetables a day on average. He finds another 200 adults who eat less than 3 servings of vegetables a day on average. The researcher looks at rates of cancer and heart disease in each group and compares both groups. In another study, the researcher finds 500 adults aged 45-60 who eat less than 3 servings of vegetables a day on average, and are willing to participate in a study. The researcher randomly assigns 250 of these adults to a diet which includes 4 servings of vegetables a day. The other 250 continue their usual habits. After 4 years, the rates of cancer and heart disease between the two groups are compared
Identify the statement that correctly states the reason for considering the first study as an observational study and second study as an experiment.
a. In the first study, the treatment is not imposed on the subjects, whereas in the second study the treatment is imposed on the subjects.
b. In the first study, the treatment is not imposed on every subject, whereas in the second study the treatment is imposed on every subject.
c. In the first study, the subjects were not randomly chosen, whereas in the second study the subjects were randomly assigned.
Answer:
a. In first study, the treatment is not imposed on the subjects, whereas in the second study the treatment is imposed on subjects.
Step-by-step explanation:
In the first study, observation are made on 300 adults who eat 3 servings of vegetables a day on average. The second study has further intensified the research which imposed treatment on the subjects. The random samples of adults are observed in both studies.
Practice Exercise 3.1 Fill in the blanks: (i) The factors of 12 are (ii) The least non-zero multiples of any number is (iii) ......... is a factor of every number. ing with Numbers
Answer:
i.)1,2,3,4,6,12
ii).the number itself
iii.)1
If 2/3 of the girls in class have brown eyes and 1/4 of the girls have blue eyes what fraction of the girls in class have neither blue or brown
The function f(x) = −x2 + 18x − 72 models the daily profit, in dollars, a gym makes for selling memberships, where x is the number of memberships sold, and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
(10 points)
Answer:
Step-by-step explanation:
The way to do this so as to streamline both the vertex and finding the zeros is to complete the square. That method will provide us with the vertex, and then we can continue on to factor from that form to find the zeros. Completing the square requires us to set the quadratic equal to 0 then move over the constant, giving us
[tex]-x^2+18x=72[/tex] The leading coefficient HAS to be a positive 1; ours is negative 1 so we factor out the negative to get:
[tex]-(x^2-18x)=72[/tex] Now we're ready to complete the square.
Take half the linear term, square it, and add it to both sides. Our linear term is 18 (from -18x; don't worry about the negative because squaring it makes it positive anyway). Half of 18 is 9, and 9 squared is 81.
BUT on the left we have that -1 sitting out front that refuses to be ignored. What we actually added on to the left side, inside the parenthesis, is -1(81) which is -81. -81 is what we add to the right since that turns out to be what we added to the left:
[tex]-(x^2-18x+81)=72-81[/tex] and we clean that up.
The reason we complete the square is because when we simplify the left side, we end up with a perfect square binomial found from taking the square root of x-squared, the first sign we come to, then the square root of 81:
[tex]-(x-9)^2=-9[/tex]. Move the constant back over to get
[tex]-(x-9)^2+9=y[/tex] telling us that the vertex is (9, 9). In the context of the problem that means that the gym sells on average 9 memberships a day and the profit it makes on average per day is $9.
To factor, we will go back one step to
[tex]-(x-9)^2=-9[/tex] and begin by dividing both sides by -1 to get
[tex](x-9)^2=9[/tex] and undo the squaring by taking the square root of both sides to get
x - 9 = ±3 so
x = 9 + 3 and
x = 9 - 3 so
x = 6 and 12
Those are the zeros. This means that if they sell either 6 or 12 memberships they have a 0 profit. That may sound strange, but in business it does often work like that...selling too many of something makes your company lose money (this is often due to the cost required by you to produce or manufacture the product).
About 12.5% of restaurant bills are incorrect. If 200 bills are selected at ran- dom, find the probability that at least 22 will contain an error. Is this likely or unlikely to occur
Answer:
0.7734 = 77.34% probability that at least 22 will contain an error. Probability above 50%, which means that this is likely to occur.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
About 12.5% of restaurant bills are incorrect.
This means that [tex]p = 0.125[/tex]
200 bills are selected at random
This means that [tex]n = 200[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 200*0.125 = 25[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.125*0.875} = 4.677[/tex]
Find the probability that at least 22 will contain an error.
Using continuity correction, this is [tex]P(X \geq 22 - 0.5) = P(X \geq 21.5)[/tex], which is 1 subtracted by the p-value of Z when X = 21.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21.5 - 25}{4.677}[/tex]
[tex]Z = -0.75[/tex]
[tex]Z = -0.75[/tex] has a p-value of 0.2266.
1 - 0.2266 = 0.7734
0.7734 = 77.34% probability that at least 22 will contain an error. Probability above 50%, which means that this is likely to occur.
Annie is opening a savings account which earns 5.2% interest compounded continuously how much will she need to deposit in the account so she has $2300 after seven years
Hi
let's call X the initial deposit.
the interest rate is 5.2 %
so each year X increase by 1.052.
so we have : X *1.052^7 =2300
X = 2300/1.052^7
X = 1612,94
please note that the deposit was rounded to the next cent. as the result would be 1612,937...
Answer:
1686.22
Step-by-step explanation:
1686.22
2300=P(1+(0.052x7))
2300=P1.364
P=2300/1.364
=1686.217...
=1686.22..
=1686 for the nearest dollar
Find y when x = 22, if y varies directly as x,
and y = 42 when x = 5.
Answer:
184.8
Step-by-step explanation:
y =kx
k=y/x
k=42/5=8.4
y=8.4*22
The polynomial p(x) = x3 – 7x - 6 has a known factor of (x + 1).
Rewrite p(x) as a product of linear factors.
p(x)
Hi there!
[tex]\large\boxed{(x -3)(x + 2)(x + 1)}[/tex]
We can use long division to find the other roots of p(x).
We know that x + 1 is a factor, so:
Set up:
Find how many times that the first term in the divisor goes into the first of the dividend. Subtract from like terms.
x² - x - 6
x + 1 | x³ + 0x² - 7x - 6
x³ + x²
0 - x² - 7x
- x² - x
0 - 6x - 6
-6x - 6
0 0
Therefore, x² - x - 6 is another factor. We can factor this further:
Find two numbers that add up to -1 and multiply into -6. We get:
-3, 2
(x - 3)(x + 2)
The entire polynomial factored is:
(x -3)(x + 2)(x + 1)
What is the largest value of A according to the division operation given above?
A)300 B)314 C)400 D)450
Answer:
Hello,
Answer B
Step-by-step explanation:
Since A=15*20+B and B<15
The max for B is 14
==> 300+14=314
what is 2x2x2x3x3 please give me answer
Answer:
The answer is 72.
I am right .
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A right rectangular prism is packed with cubes of side length fraction 1 over 4 inch. If the prism is packed with 12 cubes along the length, 8 cubes along the width, and 5 cubes along the height, what is the volume of the prism?
fraction 2 and 3 over 4 cubic inches
fraction 3 and 3 over 4 cubic inches
fraction 7 and 1 over 4 cubic inches
fraction 7 and 1 over 2 cubic inches
Answer:
7 and 1 over 2 cubic inches ( 7 1/2 in³
Step-by-step explanation:
The height = 1/4 * 5 = 1 1/4 = 1.25
The width = 1/4 * 8 = 2
The length = 1/4 * 12 = 3
Volume = 1.25 * 2 * 3 = 2.5 * 3 = 7.5
0.5 is represented as 1/2
So answer : fraction 7 and 1 over 2 cubic inches or 7 1/2 in³
if my answer is incorrect, pls correct me!
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1. 6x(-4)=
3. (-11) x 5=
4. (-12) x (-7)=
5. (-2) x (-10)
6. 4 x (-15)=
Answer:
Step-by-step explanation:
-24
-55
84
20
-60
Match each polynomial on the left with its two factors on the right.
Answer:
Hello
Step-by-step explanation:
[tex]Formula: \\\\\boxed{\Large a^3\pm b^3=(a \pm b)(a^2 \mp ab+b^2)}\\\\8x^3+1=(2x)^3+1^3=(2x+1)(4x^2-2x+1)\\\\8x^3-1=(2x)^3-1^3=(2x-1)(4x^2+2x+1)\\[/tex]
The factors of the expression 8x³ + 1 and 8x³ - 1³ will be (2x + 1) & (4x² – 2x + 1) and (2x – 1) & (4x² + 2x + 1), respectively.
What is a polynomial?A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
The expression is given below.
8x³ + 1 and 8x³ - 1³
(2x)³ + 1³ and (2x)³ - 1³
We know that the formula is given as,
a³ + b³ = (a + b) (a² – ab + b²)
a³ – b³ = (a – b) (a² + ab + b²)
Then the expression is written as,
(2x)³ + 1³ = (2x + 1) [(2x)² – 2x + 1²]
(2x)³ + 1³ = (2x + 1) (4x² – 2x + 1)
(2x)³ – 1³ = (2x – 1) [(2x)² + 2x + 1²]
(2x)³ – 1³ = (2x – 1) (4x² + 2x + 1)
The factors of the expression 8x³ + 1 and 8x³ - 1³ will be (2x + 1) & (4x² – 2x + 1) and (2x – 1) & (4x² + 2x + 1), respectively.
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What is the slope of the points (-2,7) and (2,-5)?
4
-3
-12
3
Answer:
-3
Step-by-step explanation:
Slope is equal to (-5-7)/(2-(-2)=-12/4=-3
Imagine that you are given two linear equations in slope-intercept form. You
notice that both the slopes and the y-intercepts are the same. How many
solutions would you expect for this system of equations?
O A. 1
ОВ. о
C. infinitely many
O D. cannot be determined
SURAT
Answer:
C. infinitely many
Step-by-step explanation:
If two equations in slope-intercept form have the same slope and y-intercept they must be the same line. Additionally, the solutions of a system of equations are wherever the two lines intersect. Since the lines are the same they must intersect at every point. Therefore, there are infinitely many solutions.
37. The trip between 2 towns is exactly 90 miles. You have gone 40% of this distance. How far have
you gone?
Answer:
36 miles
Step-by-step explanation:
We want to find 40% of 90 miles
40% * 90
.40 * 90
36 miles
We have to find travelled distance inorder to find this we have to find 40℅ of 90miles
[tex]\\ \Large\sf\longmapsto 90\times 40\℅[/tex]
[tex]\\ \Large\sf\longmapsto 90\times \dfrac{40}{100}[/tex]
[tex]\\ \Large\sf\longmapsto 9\times 4[/tex]
[tex]\\ \Large\sf\longmapsto 36miles [/tex]
What is the equation of a horizontal line passing through the point (-7,5)?
Oy = 5
Oy = -7
Ox=5
Ox= - 7
Answer:
1st option, y = 5
Step-by-step explanation:
when the line is horizontal, it's parallel to the x axis
Answer:
y = 5
Step-by-step explanation:
The equation of a horizontal line parallel to the x- axis is
y = c
where c is the value of the y- coordinates the line passes through
The line passes through (- 7, 5 ) with y- coordinate 5 , then
y = 5 ← is the equation of the line
Find the missing length indicated
Answer:
60
Step-by-step explanation:
Use similar triangles or the ratios from the right triangle altitude theorem.
x/36 = (64 + 36)/x
x² = 3600
x = 60
By Using 0,2,4,5,6 Write The Smallest Number And the Greatest Number
Answer:
smallest is 0 and greatest is 6
simple
Answer:
0 and 6
Step-by-step explanation:
Because 0 is means nothing.And the highest number is 6
The median age (in years) of the U.S. population over the decades from 1960 through 2010 is given by
f(t) = −0.2176t3 + 1.962t2 − 2.833t + 29.4 (0 ≤ t ≤ 5)
where t is measured in decades, with t = 0 corresponding to 1960.
(a) What was the median age of the population in the year 1970?
(b) At what rate was the median age of the population changing in the year 1970?
(c) Calculate f ''(1).
Considering the given function, we have that:
a) 28.31 years.
b) 0.3382 years a decade.
c) 2.6184.
What is the function?The median age of the U.S. population in t decades after 1960 is:
f(t) = -0.2176t³ + 1.962t² - 2.833t + 29.4.
1970 is one decade after 1960, hence the median was:
f(1) = -0.2176 x 1³ + 1.962 x 1² - 2.833 x 1 + 29.4 = 28.31 years.
The rate of change was is the derivative when t = 1, hence:
f'(t) = -0.6528t² + 3.924t - 2.933
f'(1) = -0.6528 x 1² + 3.924 x 1 - 2.933 = 0.3382 years a decade.
The second derivative is:
f''(t) = -1.3056t + 3.924
Hence:
f''(1) = -1.3056 x 1 + 3.924 = 2.6184.
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