Answer:
160 meters
Step-by-step explanation:
Before I begin, note that distance = rate * time (or d = r * t)
To solve this problem, we need to find what point these two people have the same distance. (so Janiyah covers the same distance as Connor)
So, let's set the time that Janiyah takes as x (in seconds). So, he covers
d = r * t, or 8x meters
Then, Connor's equation would be
d = r * t
d = 5x + 60 (because he got a 60 meter headstart)
Because d is the same in both equations, to solve for the amount of time they run:
8x = 5x + 60
Subtract 5x from both sides.
3x = 60
x = 20
Then, to find Janiyah's distance (you can also use Connors because the two distances are equal), put x = 20 into 8x
8x = 8 * 20 = 160
So, Janiyah ran 160 meters.
Just in case, let's check if this is correct. Connor's distance equals Janiyah's, so
5x + 60 = 160
5 * 20 + 60 = 160
100 + 60 = 160
160 = 160
True.
So, the answers are correct.
I hope this helps! Feel free to ask any questions!
Answer: 160 meters
Step-by-step explanation:
combine the like terms in the equation : 2s-4w+5+6s
To combine like terms, you have to add the same variables and all
First You have to find if the Numbers are positive or Negative
2s is positive
4w is Negative because i has Minus sigh before it
5 is Positive because it has added sigh
6s s Positive because it has added sign
Second you have to find the Like terms
2s+6s=8s
so, the new equation is
8s-4w+5.
That is the simplest
If you have questions just ask me I went through it pretty fast
Mrs. Anders gave her class 15 minutes to read. Courtney read 8 ½ pages in that time. At what rate, in pages per hour, would Courtney read?
Answer:
34
Step-by-step explanation:
15 mins is 1/4 od an hour so mulitply 8 1/2 (8.5) x 4
Answer:
First we figure out how many words in total she has to read.
This would be the (number of pages) times (number of words per page).
820 * 350 = 287000
so she has to read 287000 words
we divide this by 110 to get how long it would take for her to finish (in minutes)
287000 / 110 = 2609.09090909....
then since there are 60 minutes in an hour, we divide that number by 60
2609.09090909... / 60 = 43.48484848...
Therefore it would take her about 43.5 hours to complete her assignment.
Step-by-step explanation:
Complete this sequence of numbers such that the difference between any two adjacent numbers is the same : 3/k, _, _, 9/2k.
The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.
Let's denote the missing terms as A and B.
The given sequence is: 3/k, A, B, 9/2k.
The common difference can be found by subtracting 3/k from A or B. Therefore:
A - 3/k = B - A = 9/2k - B.
To simplify, we can equate the two expressions for the common difference:
A - 3/k = 9/2k - B.
Next, we can solve for A and B using this equation.
Adding 3/k to both sides gives:
A = 3/k + 9/2k - B.
Now, we can substitute the value of A into the equation:
3/k + 9/2k - B - 3/k = 9/2k - B.
Simplifying further, we have:
9/2k - 3/k = 9/2k - B.
Cancelling out the common terms, we find:
-3/k = -B.
Multiplying both sides by -1, we get:
3/k = B.
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Graph makes no sense to me
Answer:
(a) 0
(b) 0
(c) 1
The function is not continous at x = 9
Step-by-step explanation:
To the left and right of the point x = 9, the graph would seem to continue at f(x) = 0, however on the exact point x = 9 there is a hole in the graph allowing it to be equal to 1. Due to the hole in the graph, it is not continuous
Apologies if this is wrong its been a bit since I did calculus
Three brothers share some money. The oldest 5/11 of the money. The next boy gets gets 7/12 of the remainder. What fraction of the money does the youngest boy get?
The fraction of the money the youngest boy does get is 5x/22.
Given that, three brothers share some money. The oldest 5/11 of the money.
Let the total money be x.
Share of oldest boy = 5/11 ×x
= 5x/11
Remainder = x-5x/11
Remainder = 6x/11
The next boy gets 7/12 of the remainder.
Share of next boy = 7/12 × 6x/11
= 7x/22
Share of youngest boy = 6x/11 - 7x/22
= (12x-7x)/22
= 5x/22
Therefore, the fraction of the money the youngest boy does get is 5x/22.
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Divide: 7 5/6 ÷ 2/3 need help
To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction and then multiply it by the reciprocal of the fraction.
Step 1: Convert the mixed number to an improper fraction:
7 5/6 = (6 * 7 + 5) / 6 = 47/6
Step 2: Multiply the improper fraction by the reciprocal of the fraction:
47/6 ÷ 2/3 = 47/6 * 3/2
Step 3: Simplify the fraction if possible:
47/6 * 3/2 = (47 * 3) / (6 * 2) = 141/12
Step 4: Simplify the fraction further, if necessary:
141/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:
141/12 = (141 ÷ 3) / (12 ÷ 3) = 47/4
Therefore, 7 5/6 ÷ 2/3 is equal to 47/4 or 11 3/4.
Solve F=9/5C+32 for C.
A.F−32/9
B.5/F−32
C.9/5(F−32)
D.5/9(F−32)
Answer:
C
Step-by-step explanation:
Find the total surface area of this object.
Answer:
528 units^2solution,
Total surface area:
\(2( \frac{1}{2} \times 6 \times 8) + 6 \times 20 + 8 \times 20 + 10 \times 20 \\ = 48 + 120 + 160 + 200 \\ = 528 \: {units}^{2} \)
Hope this helps...
Good luck on your assignment..
Anu was checking her emails she casually told her friend siting next to her the ratio of unread emails in my inbox is 4:1 The total number of emails is 120 what is the number of unread emails in her inbox
In a case whereby Anu was checking her emails and she casually told her friend siting next to her the ratio of unread emails in my inbox is ratio 4:1 where the total number of emails is 120 then the number of unread emails in her inbox is 96mails.
How can the unread mails be calculated?The concept that will be used here is ratio. An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
The total mails in her box is 120
The we can represent the unread mails as 4x and read mails be 1x
This can be expressed as :
(4x+1x)=120mails
5x=120mails
x=120/5
x=24
This implies that the uread mails(4×24)
=96mails
Then the number of the read mail =(1×24)=24mails
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What is the vertical displacement of the basic graph to produce a graph of
OA Sunits down
B. 2 units down
OC units down
OD
units up
SUBMIT
The vertical displacement is of 2 units down, the correct option is B.
What is the vertical displacement?Remember that for a function f(x), a vertical displacement of N units is written in general form as:
g(x) = f(x) + N
If N > 0, the translation is upwards.
if N < 0, the translation is downwards.
Here we assume that we start with the parent cosine function:
y = cos(x)
And the transformed function is:
y = -2 - cos(x - π)
So we have some transformations, but the vertical translation is of 2 units down. So the correct option is B.
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helpppp
Lorenzo took a total of 14 quizzes over the course of 2 weeks. How many weeks of school will Lorenzo have to attend this quarter before he will have taken a total of 70 quizzes? Assume the relationship is directly proportional.
Question content area top
Part 1
A car moving at a constant speed passed a timing device at tequals
0.
After 9
seconds, the car has traveled 828
ft. Write a linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device.
A linear function rule to model the distance in feet {d} the car has traveled any number of seconds {t} after passing the timing device is
d = 92t.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a car moving at a constant speed passed a timing device at t = 0 s. After 9s, the car has traveled 828 ft.
We can write the linear function as -
y = mx
Now, we can write the slope as -
{m} = (828/9) = 92
So -
d = 92t
Therefore, a linear function rule to model the distance in feet {d} the car has traveled any number of seconds {t} after passing the timing device is
d = 92t.
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HELP ASAP! ASAPPPPPP!!! GIVING BRAINLIEST!!!
Answer:
1.2 should be right but no promises
Translate this sentence into an equation.
The product of 3 and Vidya's height is 54.
Use the variable v to represent Vidya's height.
Th equation is \(3v=54\\\).
Given,
product of 3 and vidya's height is 54
v is represented as vidya's height.
Representation of equation is as follows:
The product of 3 and vidya's height can be written as \(3*v=3v\)
and their product is 54,
\(3v=54\).
Thus, the equation is \(3v=54\\\).
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What is B^2+8b+7??
Can someone explain it step by step please?
Step-by-step explanation:
B^2+8b+7 is a quadratic expression. It can be factored as (b+7)(b+1).
To factor a quadratic expression, you can use the following steps:
1. Find two numbers that add up to the coefficient of the middle term (8) and multiply to the constant term (7).
2. Write the quadratic expression as a product of two binomials, with the two numbers you found in step 1 as the coefficients of the terms in each binomial.
In this case, the two numbers that add up to 8 and multiply to 7 are 7 and 1. So, we can factor B^2+8b+7 as follows:
(b+7)(b+1)
This means that B^2+8b+7 is equal to the product of (b+7) and (b+1).
Here is a step-by-step explanation of how to factor B^2+8b+7:
1. The coefficient of the middle term is 8.
2. The constant term is 7.
3. The two numbers that add up to 8 and multiply to 7 are 7 and 1.
4. Therefore, B^2+8b+7 can be factored as (b+7)(b+1).
9. The Super Vision cable TV/Internet/phone provider advertises a flat $100 monthly fee for all
three services for a new customer. The rate is guaranteed for 5 years. Cable Zone normally
charges $46 for monthly home phone service, $36 for monthly Internet service, and $56 for
monthly cable television.
a. How much could a customer save during the first year by switching from Cable Zone to
Super Vision?
b. Super Vision raises the rates 23% after a new customer's first year, how much will a customer
who switched from Super Vision save in the second year?
c. If Super Vision raises the rates 18% for the third year compared to the second year, which
company is cheaper for the third year?
a. $456 would be the amount a customer could save during the first year by switching from Cable Zone to Super Vision.
b. Super Vision raises the rates 23% after a new customer's first year, a customer who switched from Super Vision save $180 in the second year.
c. Super Vision raises the rates 18% for the third year compared to the second year, for the third year, Cable Zone would be cheaper.
a. To calculate how much a customer could save during the first year by switching from Cable Zone to Super Vision, we need to compare the costs of the two providers.
Cable Zone charges $46 for monthly home phone service, $36 for monthly Internet service, and $56 for monthly cable television. Therefore, the total cost per month with Cable Zone is:
$46 (home phone) + $36 (Internet) + $56 (cable television) = $138
Super Vision, on the other hand, offers all three services for a flat $100 monthly fee. So, the customer would save:
$138 (Cable Zone cost) - $100 (Super Vision cost) = $38 per month
Therefore, during the first year, the customer could save:
$38 (monthly savings) * 12 (number of months) = $456
b. After the first year, Super Vision raises the rates by 23%. The new monthly fee would be:
$100 (original fee) + 23% (rate increase) * $100 (original fee) = $123
To calculate the savings in the second year, we need to compare the new Super Vision fee to the cost with Cable Zone:
$138 (Cable Zone cost) - $123 (Super Vision cost) = $15 per month
Therefore, in the second year, the customer would save:
$15 (monthly savings) * 12 (number of months) = $180
c. If Super Vision raises the rates by 18% for the third year compared to the second year, we need to calculate the new monthly fee. The new Super Vision fee would be:
$123 (second-year fee) + 18% (rate increase) * $123 (second-year fee) = $145.14
To determine which company is cheaper for the third year, we compare the new Super Vision fee to the cost with Cable Zone:
$138 (Cable Zone cost) - $145.14 (Super Vision cost) = -$7.14
In this case, the Super Vision cost is higher than the Cable Zone cost by $7.14 per month. Therefore, for the third year, Cable Zone would be cheaper.
Overall, during the three-year period, the customer would save a total of $456 (first year) + $180 (second year) = $636 by switching to Super Vision.
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Draw the image of quadrilateral ABCD under the translation (x,y) (x-7,y+1).
The translated figure will be entirely within the 3rd quadrant of the graph.
We have, translation (x, y)--> (x-7,y+1).
Here, the notation (x, y) ⇒ (x-7, y+1) means that each x-coordinate has 7 subtracted from it.
Additionally, each y-coordinate has a 1 added to it because of the notation. Point B's y-coordinate is -3. It becomes -2 by adding 1.
As a result, point B's image will be at (-7, -2), 7 units to the left and 1 unit to the upper right of B.
Thus, the translated figure will be entirely within the 3rd quadrant of the graph.
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II) EXERCISE 10–3 Direct Labour Variances
SkyInc provides in-flight meals for a number of major airlines. One of the company’s products is stuffed cannelloni with roasted pepper sauce, fresh baby corn, and spring salad. During the most recent week, the company prepared 6,000 of these meals, using 1,150 direct labour-hours. The company paid these direct labour workers a total of $11,500 for this work, or $10 per hour.
According to the standard cost card for this meal, it should require 0.20 direct labour- hours at a cost of $9.50 per hour.
2. Break down the difference computed in (1) above into a labour rate variance and a labour efficiency variance, and perform the corresponding accounting records.
The total Variance above the standard labor cost $100
Standard cost to prepare the meal at actual quantity
6,000 x 0.20 = 1,200 x $9.50 = $11,400
Actual incurred = 11500
labor rate variance
11,500 actual - (1,150 actual hours x $9.50 standard rate) = -$575 u
labor efficiency variance =(1,150 actual hours x $9.50 standard rate) - $11,400 = 475 f
The variance contains two components, an unfavorable rate variance, offset by a favorbale efficiency variance. The rate variance is calculated by comparing the actual amount paid to the actual hours at the standard rate.
Add the labor rate variance of $575 and the efficiency variance of ($475) and you get a total variance of $100 above the standard labor cost.
So
The total Variance above the standard labor cost $100
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Rick Rich owns a Mercedes dealership. Mercedes has 5 models, 4 standard options packages, and 5 colors. If Rick wants to immediately be able to deliver any car (model, option package, color), how many cars must Rick have on hand?
Rick would need to have at least 100 cars on hand to immediately be able to deliver any car (model, option package, color).
To immediately deliver any car, Rick Rich's dealership must have all possible combinations of Mercedes models, option packages, and colors in stock.
With five models, four option packages, and five colors, there are 5 x 4 x 5 = 100 possible combinations.
Therefore, Rick would need to have at least 100 cars on hand, each representing a unique combination of model, option package, and color. It's worth noting that having exactly 100 cars on hand would only allow Rick to deliver one of each possible combination, so it may be prudent to have additional inventory on hand to meet demand for more popular combinations.
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GUYS PLEASE HELP ME OUT???
Using the concept of linear pair we get the measure of angle a that is equal to 94 degree.
Two lines are given k and m
In the below attached image we can see there are two lines k and m that are intersecting .
lines that intersect meet at a common point.
Here we will use the concept of Linear pair of angles.
When two lines intersect with each other then some angles are formed (opposite angles and adjacent angles).
If the angles are adjacent to each other then the angles are known as linear pair of angles.
Using the property that the Sum of angles of linear pair is always equal to 180 degree -------A
From the figure
86 + a = 180 (From A)
a= 180-86
a= 94
So the measure of the angle a is 94 degree.
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Hint 1
Choose the correct label for the point on the boxplot represented by the question mark
O 01
O Q3
OM
O min
Омах
QR
O Range
None of the above
Answer:
None of the above.
Step-by-step explanation:
The box plot given has an asterisk which represents an outlier in the data set plotted. This outlier is an extreme data set value which is obviously the maximum value in the data set.
The question mark can be regarded as the highest observation that doesn't take the outlier observation into consideration.
Therefore, none of the options given is the correct label for the point on the box plot represented by the question mark.
Solve |2x+4|≥22, then graph the solution.
Answer:
\((2x + 4) \geqslant 22 \\ 2x = 18 \\ x = 9 \\ \\ - (2x + 4) \geqslant 22 \\ 2x + 4 \leqslant - 22 \\ 2x \leqslant - 26 \\ x \leqslant - 13\)
For each diagram, write and solve an inequality for x.
7.
2x - 5
X
What is the answer
For the given diagram the inequality for x is x ≥ 6.
What is inequality?If two values differ, it can be determined whether one is larger, smaller, or simply not equal to the other.
A and B claim that they are not equal.
A must be less than B if A = B.
An is greater than b when a > b. These two constitute strict inequality.
A must be less than or equal to b if a and b are divided.
An is greater than b if a and b are equal.
We have given a right-angled triangles with hypotenuse 2x - 5 and base x
Using the Pythagoras theorem
c² = a² + b²
We know hypotenuse is always greater than base with that in mind lets assume x to be 1
then 2x - 5
= 2(1)-5
= -3 which is smaller than 1
It means x at least need to be equal to 6 or greater than 6 to Pythagoras theorem to be possible
When x = 6
= 2(6)-5
= 7 hypotenuse
Gives the inequality
x ≥ 6
Thus, For the given diagram the inequality for x is x ≥ 6.
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A bag contains 250 cubes that are black, yellow and white. A student randomly selects a cube without looking and replaces it in the bag. If the student selected 15 black cubes, 6 yellow cubes and 4 white cubes, which of the options below show a reasonable estimate for the total number of each color cube in the bag? Select all that apply. A) 40 white cubes B) 120 yellow cubes C) 150 black cubes D) 80 white cubes E) 60 yellow cubes
Answer: It's possible that A, C, and D are the correct answers.
Step-by-step explanation:
40+60=100
100+150=250
At the Fisher farm, the weights of zucchini squash are Normally distributed, with a mean of 5 ounces and a
standard deviation of 0.7 ounces. Which weight represents the 8th percentile?
Find the z-table here.
O 3.56 ounces
O 4.01 ounces
O 5.59 ounces
O 5.98 ounces
Answer:
4.01
Step-by-step explanation:
Mary invested $200 for 3 years at 5% per annum. John invested $300 at the same rate. If they both received the same amount of interest how much did john invest???
Answer:
Step-by-step explanation:
Assume that a random sample of 4 Goldfinch birds are going to be used to test the above hypothesis. Compute the largest value of the sample mean, that will allow the experimenter reject the null and prove the alternative at significance level 0.01. For this problem, make sure that your solution includes all steps of your computation. You will not earn points if you just use a formula
This question is incomplete, the complete question is;
Assume that body masses of Goldfinch birds follow a normal distribution, with a standard deviation equal to 0.04 oz. An ornithologist who would like to make some inference about the average body mass of the Goldfinch birds. In particular, at a significance level of 0.01, she would like to test the null hypothesis H₀: Average body mass of the Goldfinch birds is 0.5 oz, against the alternative claim that average body size is less than 0.5 oz.
Assume that a random sample of 4 Goldfinch birds are going to be used to test the above hypothesis. Compute the largest value of the sample mean, that will allow the experimenter reject the null and prove the alternative at significance level 0.01. For this problem, make sure that your solution includes all steps of your computation. You will not earn points if you just use a formula
Answer: the largest value of the sample mean that will enable the experimenter to reject the null hypothesis is 0.4534 oz.
Step-by-step explanation:
Let us consider testing a hypothesis about a population mean with population standard deviation that is known,
Let the average body mass of the Goldfinch bird be μ^μ
Now our hypotheses are will be;
H₀ : μ = 0.5 and
H₁ : μ < 0.5
For the test, we shall use the z statistic which will be
z = (x"-μ)/(σ/√n)
Now given that;
σ = 0.04 and n = 4
sample mean x" = ?
Now in order to be able to reject the null hypothesis, the p-value should be ≤ α = 0.01.
so to find the largest value of sample mean, we will use the maximum of p-value that is 0.01.
For a p-value = 0.01 at the lower tail (which is the percentile for z),
the corresponding z will be -2.33
so we substitute our values into our formula
z = (x"-μ)/(σ/√n)
z(σ/√n) = (x"-μ)
-2.33(0.04/√n) = (x"-0.5)
-0.0466 = x" - 0.5
x" = 0.5 - 0.0466
x"= 0.4534
therefore the largest value of the sample mean that will enable the experimenter to reject the null hypothesis is 0.4534 oz.
Joey’s math average in the first quarter was an 83. In the second quarter, his average was 93. What was the approximate percent increase in his math average?
The approximate percent increase in his math average is 12%
How to find the approximate percent increase in his math average?
A percentage is defined as the ratio that can be expressed as a fraction of 100.
percent increase in math average = (difference in average/initial average) * 100
percent increase in math average = (93 - 83)/83 * 100
percent increase in math average = 10/83 * 100
percent increase in math average = 12%
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What is (x³-8x² + 6x +41) ÷ (x-4)
Step 1: Write the dividend and divisor:
\(\sf\:\frac{{x^3 - 8x^2 + 6x + 41}}{{x - 4}} \\ \)
Step 2: Divide the first term of the dividend by the first term of the divisor:
\(\sf\:\frac{{x^3}}{{x}} = x^2 \\ \)
Step 3: Multiply the divisor (x - 4) by the result (x^2):
\(\sf\:(x - 4) \cdot (x^2) = x^3 - 4x^2 \\ \)
Step 4: Subtract the result from the original dividend:
\(\sf\:(x^3 - 8x^2 + 6x + 41) - (x^3 - 4x^2) = -4x^2 + 6x + 41 \\ \)
Step 5: Bring down the next term from the dividend:
\(\sf\:\frac{{-4x^2 + 6x + 41}}{{x - 4}} \\ \)
Step 6: Repeat steps 2-5 with the new dividend:
\(\sf\:\frac{{-4x^2}}{{x}} = -4x \\ \)
\(\sf\:(x - 4) \cdot (-4x) = -4x^2 + 16x \\ \)
\(\sf\:(-4x^2 + 6x + 41) - (-4x^2 + 16x) = -10x + 41 \\ \)
Step 7: Bring down the next term from the dividend:
\(\sf\:\frac{{-10x + 41}}{{x - 4}} \\ \)
Step 8: Repeat steps 2-5 with the new dividend:
\(\sf\:\frac{{-10x}}{{x}} = -10 \\ \)
\(\sf\:(x - 4) \cdot (-10) = -10x + 40 \\ \)
\(\sf\:(-10x + 41) - (-10x + 40) = 1 \\ \)
Step 9: There are no more terms to bring down, so the division is complete.
Step 10: Write the final result:
The quotient is \(\sf\:x^2 - 4x - 10\\\) and the remainder is 1.
Therefore, the division of \(\sf\:(x^3 - 8x^2 + 6x + 41) by (x - 4) \\\) is:
\(\sf\:(x^3 - 8x^2 + 6x + 41) ÷ (x - 4) \\ \) \(\sf\:= x^2 - 4x - 10 + \frac{{1}}{{x - 4}} \\ \)
Solve the equation for y 10x - 5y = 15