The nonzero vector orthogonal to the plane through the points P,Q and R is -7i + 7j -21k and the area of the triangle is 11.6 square units.
(a)Given points are P(-1,3,1) , Q(0,7,2) and R(4,2,-1)
PQ = Q - P
= (0 - (-1))i + (7 - 3)j + (2 -1)k
=i + 4j + k
PR = R - P
= (4 - (-1))i + (2 - 3)j + (-1 - 1)k
5i -j - 2k
The orthogonal vector is PQ x QR
[tex]\left[\begin{array}{ccc}i&j&k\\1&4&1\\5&-1&-2\end{array}\right][/tex]
(-8 + 1)i - (-2 - 5)j + (-1 - 20))k
-7i + 7j - 21k
Therefore the nonzero vector orthogonal to the plane through the points P,Q and R is -7i + 7j - 21k
(b) The area of the triangle with the vertices P,Q and R is the half of the length of the cross product of PQ and QR.
Area = 1/2| PQ x QR|
= 1/2 √(7² + (-7)² + (-21)²)
= 1/2 √(49 + 49 + 441)
= 1/2 (23.21)
= 11.60
= 11.60 square units.
Therefore The non zero vector is -7i + 7j - 21k and the area of the triangle is 11 .6 square units.
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h is a trigonometric function of the form h(x)=acos(bxc)+d. Below is the graph of h(x) The function has a maximum point at (3,6) and a minimum point at (6.5,-9) find the formula for h(x). Give an exact expression.
h(x)=
*from klan academy*
Please Help URGENT
The exact expression for the cosine function is given as follows:
h(x) = 7.5cos(2π/7(x + 0.5)) - 1.5.
How to define the cosine function?The definition of the cosine function is given as follows:
h(x) = acos(b(x - c)) + d.
The parameters of the function are given as follows:
a: amplitude.b: The period is of 2π/B.c: phase shift.d: vertical shift.The difference between the maximum value and the minimum value is of 6 - (-9) = 15, hence the amplitude is obtained as follows:
a = 15/2 = 7.5.
From the graph given at the end of the answer, the period is of 7 units, hence:
2π/b = 7
7b = 2π
b = 2π/7.
The minimum value should be at x = 0, however it is at x = -0.5, hence the phase shift is given as follows:
c = -0.5.
Considering the amplitude of 7.5, without vertical shift the function would oscillate between -7.5 and 7.5, however is oscillates between -9 and 6, hence the vertical shift is given as follows:
d = -1.5.
Thus the function is defined as follows:
h(x) = 7.5cos(2π/7(x + 0.5)) - 1.5.
Missing InformationThe graph of the function is given by the image shown at the end of the answer.
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1. Gordon estimates that the ramp will be 6 inches tall when it is 60 inches
long. Explain the error that he made and correct the error.
Answer:
it's 0.25 for the first one
You can spend at most $8 on potatoes and carrots for a stew. Potatoes cost $2 per pound,
and carrots cost $1 per pound. Write an inequality that represents the amounts of potatoes
and carrots you can buy. Let x = pounds of potatoes and let y = pounds of carrots.
Answer:
[tex]2x + y \leq 8[/tex]
Step-by-step explanation:
since potatoes cost $2 they are represented as 2x
Carrots cost $1 and are simply y
find the equation of the linear function represented by the table. x 1,2,3,4 y 1,6,11,16
Answer: y = 5x - 4
Step-by-step explanation: The equation of a linear function can be found by using the slope-intercept form, which is y = mx + b, where m is the slope of the line and b is the y-intercept (i.e., the point at which the line crosses the y-axis).
To find the equation of the linear function represented by the table, we can use the values from the table to calculate the slope. The slope is calculated as the change in y over the change in x, or (y2 - y1)/(x2 - x1). Using the values from the table, we can calculate the slope as (6 - 1)/(2 - 1) = 5/1 = 5.
Next, we can use the slope and one of the points from the table to find the y-intercept. If we use the point (1,1), we can substitute the values into the slope-intercept form to get 1 = 5*1 + b, so b = -4.
Therefore, the equation of the linear function represented by the table is y = 5x - 4.
The two cotton processing companies are producing different products and those are sold out the products one year before. The sold sum of both the two companies salaries are $44,000,000. The sold price of company x is 1000 more than the other. Therefore, find the value of each company's product sold price by framing a linear equation?
The final value of company x sold price is; $22,000,500
The final value of company y sold price is; $21,999,500
How to solve Linear equation word problems?Let the amount of sold out products in company x and company y be denoted by a
Now, we are told that sum of both the two companies salaries are $44,000,000.
Now, the sold price of company x is 1000 more than the other.
Thus;
Sold price of company y = y
Sold price of company x = 1000 + y
Thus;
1000 + y + y = 44000000
1000 + 2y = 44000000
2y = 44000000 - 1000
2y = 43,999,000
y = 43,999,000/2
y = $21,999,500
Thus;
Sold price of company x = $21,999,500 + $1000 = $22,000,500
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Q3. (b)
The length of human pregnancies from conception to birth approximate a normal
distribution with a mean of 266 days and a standard deviation of 16 days.
(i). What percentage of all pregnancies will last less than 240 days?.
Soln.
Answer:
5.2%
Step-by-step explanation:
You randomly observe purchases at a candy store and record the weight of each bag of candy
with 100 different customers. You find the proportion of weights greater than 2 pounds. Is
investigating this sample proportion the same as investigating the sampling distribution of the
proportion?
Answer:
OptionB)
Step-by-step explanation:
→→When you are talking about sample proportion You are considering a Single ,set of same kind of Data,Like body weight of Students in a class, from which you are taking out samples for Observation.
For example, A colony is being studied whether each human in that colony is healthy or not by checking their body mass index.
→→When we are investigating or considering Sampling Distribution we consider two different sets or kinds of Data set Possessing Similar Characteristics because we have to compare these two sets of Data.
For example , Take two colonies A and B , Check their honesty by observing how many floors they have made in their Plot.Whether they care or don't care about their Surrounding or Mother Earth by looking, if number of floors exceeds than 2 i.e ground floor and first floor , it means Dishonest , if maximum number of floor =2 ,it means honest.
these statements are the congruence statements for right triangles: ha, ll, la, and hl. you will need to use them for congruence statements. match the abbreviation to its description. for right triangles: 1. a hypotenuse and a leg define congruence. hl 2. a hypotenuse and an acute angle define congruence. la 3. a leg and an acute angle define congruence. ll 4. two legs define congruence. ha
Answer:
HA:A hypotenuse and an acute angle define congruence
HL:A hypotenuse and a leg define congruence
LL: Two legs define congruence
LA:A leg and an acute angle define congruence
Step-by-step explanation:
HA theorem:
When hypotenuse and one acute angle of a triangle is congruent to hypotenuse and one acute angle of a other triangle, then the triangles are congruent
HL theorem:
When hypotenuse and one leg of a triangle is congruent to hypotenuse and one leg of other triangle, then the triangles are congruent
LL theorem:
When two legs of a triangle is congruent to the two legs of other triangle, then the triangles are congruent
LA theorem:
When one leg and one acute angle of a triangle is congruent to one leg and one acute angle of other triangle, then the triangle are congruent
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Which angles are consecutive interior angles?
By using the properties of angle, it can be concluded that
[tex]\angle QPS[/tex] and [tex]\angle TSP[/tex] are consecutive interior angle
What is angle?
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.
[tex]\angle QPS[/tex] and [tex]\angle TSU[/tex] are not consecutive interior angle as [tex]\angle PST[/tex] falls in between
[tex]\angle QPS[/tex] and [tex]\angle RSU[/tex] are not consecutive interior angle as [tex]\angle RSU[/tex] is an exterior angle
[tex]\angle QPS[/tex] and [tex]\angle TSP[/tex] are consecutive interior angle
[tex]\angle QPS[/tex] and [tex]\angle OPN[/tex] are not consecutive interior angle as [tex]\angle OPN[/tex] is an exterior angle
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two events, a and b are independent if and only if . recall that a reorganization of the multiplication rule will yield . suppose for some events a and b, . which of the following statements is true of a and b? select an answer and submit. for keyboard navigation, use the up/down arrow keys to select an answer. a events a and b are independent since and . b events a and b are not independent, but they are mutually exclusive since . c events a and b are independent since ; however . d events a and b are not independent since and .
Option- A is correct that is event a and b are independent when consider some events a and b rearranging the multiplication rule will result in.
Given that,
If and only if, two events, a and b, are independent. Remember that rearranging the multiplication rule will result in. Consider some events a and b.
We have to find which of the following claims about a and b is true.
We know that,
We have if the occurrence of event A has no bearing on the probability that event B will also occur, then the two events A and B are said to be independent.
P(A and B) = P(A) P(B) can be used to numerically describe the probability of two separate events.
As a result, we can draw the conclusion that two events, a and b, are independent if and only if they are.
Therefore, Option- A is correct that is event a and b are independent when consider some events a and b rearranging the multiplication rule will result in.
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A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. Suppose that in February 2012, a sample of 1,000 adults showed 410 indicating that their financial security was more than fair. In February 2010, a sample of 1,100 adults showed 385 indicating that their financial security was more than fair.
(a)
State the hypotheses that can be used to test for a significant difference between the population proportions for the two years. (Let p1 = population proportion saying financial security more than fair in 2012 and p2 = population proportion saying financial security more than fair in 2010.)
H0: p1 − p2 = 0
Ha: p1 − p2 ≠ 0
H0: p1 − p2 > 0
Ha: p1 − p2 ≤ 0
H0: p1 − p2 ≠ 0
Ha: p1 − p2 = 0
H0: p1 − p2 ≥ 0
Ha: p1 − p2 < 0
H0: p1 − p2 ≤ 0
Ha: p1 − p2 > 0
The hypotheses that can be used to test for a significant difference between the population proportions for the two years is H0 :- P1 = P2
How to calculate the hypotheses?
In math, the process of calculating the hypotheses is to select a statistic based on a sample of fixed size, calculate the value of the statistic for the sample and then reject the null hypothesis if and only if the statistic falls in the critical region.
Here we know that certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. Suppose that in February 2012, a sample of 1,000 adults showed 410 indicating that their financial security was more than fair. In February 2010, a sample of 1,100 adults showed 385 indicating that their financial security was more than fair.
And we need to find the hypotheses that can be used to test for a significant difference between the population proportions for the two years.
Here let us consider P1 refers population proportion saying financial security more than fair in 2012 and P2 refers population proportion saying financial security more than fair in 2010.
As per the definition of the hypotheses, the resulting hypotheses is written as,
=> H0 :- P1 = P2
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use a proof by contraposition to show that for integers m and n if m n is even then m is even or n is even
The contrapositive is true
Proving a contraposition involves proving that the contrapositive of a statement is true. The opposite of "if m n is even then m is even or n is even" is "if m is not even and n is not even then m n is not even".
To prove this statement by a proof by contrast, first assume that m is not even and neither is n. This means that both m and n are odd.
Since m and n are odd, m n is also odd. This can be expressed as:
If m and n are odd, we can write m as;
2k + 1 and n as 2l + 1 for integers k and l.
Then mn = (2k + 1)(2l + 1) = 4kl + 2k + 2l + 1 = 2(2kl + k + l) + 1,
which is odd. Therefore, m n is not even if m is not even and n is not even.
It turns out that the opposite of the original statement is true, so the original statement must also be true. Therefore, if m n is even, then we can say that that m is even or n is even using a proof by contrast.
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When conducting a hypothesis test for a given sample size, if the probability of a Type I error decreases, then the _____________.
a. probability of incorrectly accepting the null hypothesis decreases
b. probability of Type II error decreases
c. probability of incorrectly accepting the null hypothesis increases
d. probability of incorrectly rejecting the null hypothesis increases
The probability of a Type I error is the probability of incorrectly rejecting the null hypothesis. When the probability of a Type I error decreases, the probability of a Type II error, It decreases the likelihood of choosing the null hypothesis wrongly.
When conducting a hypothesis test for a given sample size, a Type I error is the probability of incorrectly rejecting the null hypothesis. This means that the null hypothesis is true, but the hypothesis test incorrectly rejects it. A Type II error is the probability of incorrectly accepting the null hypothesis. This means that the null hypothesis is false, but the hypothesis test incorrectly accepts it. When the probability of a Type I error decreases, it means that the hypothesis test is more accurate in correctly rejecting the null hypothesis when it is false. This in turn means that the probability of a Type II error also decreases, as the test is more accurate in correctly accepting the null hypothesis when it is true. In other words, when the probability of a Type I error decreases, the probability of a Type II error decreases as well.
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Determine whether the rule represents an exponential function. Explain why or why not.
Y=-2•x^7 WILL MARK BRAINLIEST
A. Since the independent variable X is not the exponent, y=-2•x^7 does not represent an exponential function.
B. Since the independent variable X is not the base, y=-2•x^7 does not represent an exponential function.
C. Since the independent variable x is the base, y=-2•x^7 does represent an exponential function.
D. Since the independent variable X is the exponent, y=-2•x^7 represents an exponential function.
The equation y = - 2 · x⁷ is not an exponential function because the independent variable x is the base of the formula instead of being its exponent. (Correct choice: A)
Does a given expression represent an exponential function?
In this problem we need to determine whether the equation y = - 2 · x⁷ represent an exponential function or not. Exponential functions are expressions of the form:
y = b · aˣ
Where:
a, b - Real coefficients. (b - Value when x = 0, a - Base)x - Independent variable.y - Dependent variable.By direct comparison we notice that the given equation is not an exponential function as the independent variable x is not the exponent of the expression and it is the base instead. The expression y = - 2 · x⁷ is a power function, not an exponential function.
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Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.]
f(x) = 7(1 − x)−2
f(x) =
[infinity] sum.gif
n = 0
Find the associated radius of convergence R.
R =
The radius of convergence R of the given function f(x) = (-1)^n(1 - x)² be,
R = 1/2.
Given, a function f(x)
f(x) = (-1)^n(1 - x)²
we have to find the radius of convergence R of the given function,
first will find the (n+1)th term of the given function
as, an = (-1)^n(1 - x)²
then an+1 = (-1)^(n+1)(1 - x)²
to find the radius of convergence, we will find
lim x->∞ an+1/an
lim x->∞ ((-1)^(n+1)(1 - x)²)/((-1)^n(1 - x)²)
On solving the limits, we get
lim x->∞ an+1/an = 2x
then R = 1/2
as, -1/2 < x < 1/2
so, the radius of the convergence be, 1/2
Hence, the radius of the convergence be, 1/2
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Help me please help me
Answer:
125 -v³ = (5 -v)(v² +5v +25)
Step-by-step explanation:
You want to factor the expression 125 -v³.
FactorsFrom your knowledge of the cubes of small integers, you recognize that 125 = 5³. That lets you see this expression is the difference of cubes, which has a factor pattern:
a³ -b³ = (a -b)(a² +ab +b²)
Your difference factors as ...
5³ -v³ = (5 -v)(5² +5v +v²)
125 -v³ = (5 -v)(v² +5v +25)
Find the average rate of change for the function over the given interval y=x^2+9x between x=3 and x=7.
Answer:
average rate of change = 19
Step-by-step explanation:
the average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [ 3, 7 ] and y = f(x) , then
f(b) = f(7) = 7² + 9(7) = 49 + 63 = 112
f(a) = f(3) = 3² + 9(3) = 9 + 27 = 36
then
average rate of change = [tex]\frac{112-36}{7-3}[/tex] = [tex]\frac{76}{4}[/tex] = 19
Travis, Jessica , and robin are collecting donations for the school band. Travis wants to collect 20% more than jessica and robin wants to collect 35% more than travis. If the students meet there goals and Travis collects $43 how much money did they collect in all
They collected $134.45 and we can find this using percentage.
Travis = $43
Jessica = 43 - (43 × 20%) = $34.4
Robin = 43 + (43 × 35%) = $58.05
Percentage (%):
In maths percentage is the value of ratio that shows the fraction of 100.percent means per 100.It does not have any units.Percentage is denoted by %It is also known as per cent.In order to find percent, we use the formula (original number/ another number) multiply by 100.It has a variety of uses in mathematics.Percentage increase and decrease can be calculated by computing the difference between the two values and comparing to the initial value.To know more about Percentage:
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hroughout the 2016 presidential election primaries, millennials (those aged 20 to 36 years) consistently supported senator bernie sanders over secretary hillary clinton. according to the 2016 gallup poll of 1,754 millennials, 55% had a favorable opinion of sanders compared with hillary clinton (38%). calculate the 90% confidence interval for both reported percentages. step-by-step calculation for hillary clinton (4 points)
The range of 90% confidence will be: (0.5305,0.5695)
What is percentage?
The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.
Given,
Sample percentage equals 0.55
z = 1.645 for 90% confidence.
Therefore, the range of 90% confidence will be:
(0.5305,0.5695)
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Royal Co. receives a dividend of $4.88 per share. Today the closing price of the stock is $59.95. The current stock yield to the nearest tenth of a percent is: 8.1% 8.0% 8.2% 8.3% None of these
Receiving $4.88 dividend out of the closing stock price of $59.95, means that the stock yield is 8.1%
Dividend is defined as a distribution of payment by a company to its shareholders that is originated from the company's profit and is payable to the shareholders every quarter in a given year, while stock yield is defined as an income generated by the stock being held by the shareholders.
To determine the percentage of stock yield, we will need to divide the closing price of the stock which is $59.95 with the amount of dividend distributed for each stock held which is $4.88, and the calculation is as follows:
59.95/4.88×100%=8.1%
Therefore the stock yield is 8.1%
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Find the distance between (6,-2) and (1,2)
Answer: [tex]\displaystyle d=\sqrt{41} \approx 6.4[/tex]
Step-by-step explanation:
We will use the distance formula to help us solve (see attached). Let (6, -2) be point one and (1, 2) be point two.
[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]
[tex]\displaystyle d=\sqrt{(1-6)^2 +(2--2)^2}[/tex]
[tex]\displaystyle d=\sqrt{(-5)^2 +(4)^2}[/tex]
[tex]\displaystyle d=\sqrt{25 +16}[/tex]
[tex]\displaystyle d=\sqrt{41} \approx 6.4[/tex]
41 is a prime number, so this is the simplest radical form.
Question 2
What is the length of DE? (number only)
The length of DE is 6.3
Similar triangles are triangles that have a similar appearance but differ in size.
Two triangles are similar if their angles are the same (corresponding angles) and their sides have the same ratio or proportion (corresponding sides)
If two triangles are similar, it means that their corresponding angle pairs are all equal.All triangle corresponding sides are proportional.The " ~ " symbol is used to represent similarity.
According to the question,
In ΔABC and ΔDBE,
(1) ∠B = ∠B (common)
(2) ∠ACB = ∠DEB (opposite sides are equal)
(2) ∠CAB = ∠ECB
Therefore , ΔABC ~ ΔDBE
By using similar triangle property
The ratio of correspond sides are equal ,
AB/BD = BC/BE = AC/DE
=> 2/1 = AC/DE
=> 12.6 / DE = 2/1
=> DE = 12.6/2
=> DE = 6.3
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Question 9
determine the number of n digit numbers with all digits even, such that 2 and 4 each occur a nonzero, odd number of times.
According to the question asked the number of digits with all digits even can be found as:
aₙ = 6ⁿ + 2.3ⁿ + 1(n≥0)
Given:
let the number be aₙ.
The number aₙ equals the number of n permutations at the multiset S
where S = { ∞ 2, ∞ 4, ∞ 6, ∞, 8, ∞ 10} on which 2 and 4 occurs
a non zero even number at times.
The exponential generating function have a₀, a₁, a₂,....aₙ
f'(x) = (1+x²/2! + x⁴/4!+...)ⁿ
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assume that the heights of of adult males in a certain region are normally distributed. the heights (in inches) of 20 randomly selected adult males from this region are listed below: 70 72 71 70 69 73 69 68 70 71 67 71 70 74 69 68 71 71 71 72 use this sample data and a .05 significance level to test the claim that the variance of all heights in this region is less than 6.25.
The sample variance is 2.976 , which means it's lesser than 6.25. We calculate this using the standard method.
Given:
Sample data is 0.05
The sample size is 20.
And ,
The hypotheses are:
H0: sigma^2 = 6.25 (>=)
Ha: sigma^2 < 6.25
The critical value is 10.117. If the test statistic is less than this value, we'll reject the null hypothesis. We Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. For a mnemonic device, remember—when the p-value is low, the null must go.
The test statistic is:
2.976 * 19 / 6.25 = 9.047.
So we reject the null hypothesis. The variance is not 6.25, which means it is lesser then 6.25
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16. Find 2,075 ÷ 7. A 295 B 296 R1 C 296 R3 D 304 R5
Answer:
C. 296 R3
Step-by-step explanation:
In order to find the quotient, lets use long division:
296 R 3
_________
7 | 2075
- 14
__
67 ==> drop 7 from 2075
- 63
__
45 ==> drop 5 from 2075
- 42
__
3
Does y = x2 + 1 represent a linear or nonlinear function? Explain.
Answer: the function is nonlinear
Step-by-step explanation:
y = x2 + 1 is a nonlinear equation because for it to be an linear question it must be the following
Linear:
2x-1=y
y=2x-1
nonlinear
y = x2 + 1
Linear equations are a constant slope ( straight line ) and nonlinear equations has a slope that varies between points so y = x2 + 1 is an non-linear equation because it has an slope that varies between points.researcher is using a Kruskal-Wallis test to evaluate the difference between three treatment conditions using a sample of n-8 in each treatment. What value of H is necessary to conclude that there is a significant difference among the treatments using a 05 Select one O a. H25.99 Ob. H2 347 c H2 1.96 O d. H 2080
C. H2 1,96
To establish whether there is a significant difference between treatments using the Kruskal-Wallis test, the calculated value of H should be compared to the critical values in the table of H values. The critical value of H to use depends on the significance level chosen for the test (0.05 in this case).
Using a significance level of 0.05, the critical value of H for a sample size of n-8 for each treatment is approximately H2 1.96. That is, if the calculated H value is greater than 1.96, we can conclude that there is a significant difference between the treatments.
Hence, the correct answer in this case is c. H2 1,96
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Diana averages 6 mph walking
to school. Averaging 35 mph on
the way back home by car, she
takes } hour less time.
How far is the school
from her home?
If Diana averages 6 mph walking to school. The distance from the school to her home is 5.4 miles.
What is distance?Distance can be defined as how far an object is from another object.
Formula for Distance
Distance = Speed × Time
Solving for t (time) to walk to school
6t = 35 (t-.75)
6t = 35t - 26.25
Collect like terms
29t= 26.25
Divide both side by 29t
t = 26.25/29
t= .9
t=54 minutes
Solving for Distance (d)
d = 6× .9
d = 5.4 miles
Therefore the distance is 5.4 miles.
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The complete question is:
Diane averages 6 mph walking to school. Averaging 35 mph on the way back home by car, she takes 3/4 hour less time. How far is the school from her home?
Please help I’m going to fail i need help please
The volume of the figure can be calculated by adding the volumes of the two rectangular prisms. The first rectangular prism has dimensions 12 in x 10 in x 2 in, so its volume is 12102 = 240 in^3. The second rectangular prism has dimensions 10 in x 7 in x 21 in, so its volume is 10721 = 1540 in^3. The total volume of the figure is 240 in^3 + 1540 in^3 = 1780 in^3.