To solve the system of inequalities, we find the values of x that satisfy both conditions: x > 3 and x < -1.
Explanation:To solve this problem, we need to find the values of x that satisfy the given inequalities:
4x+2 > 14
-21x+1 > 22
For the first inequality, subtracting 2 from both sides gives us:
4x > 12
Dividing both sides by 4, we get:
x > 3
For the second inequality, subtracting 1 from both sides gives us:
-21x > 21
Dividing both sides by -21 (and flipping the inequality sign), we get:
x < -1
Therefore, the values of x that satisfy both inequalities are:
x > 3 and x < -1
What is the expression of one less than the quotient of four and a number x
contractor A estimated a job would cost $54,000 to complete in 90 days. contractor B estimated he could complete the same job for $49,500 in 120 days. how much per day does each contractor charge
Contractor A estimated a job would cost $54,000 to complete in 90 days.
Per day charge of Contractor A = $54,000 / 90 = $ 600 / day
Contractor B estimated he could complete the same job for $49,500 in 120 days.
Per day charge of Contractor A = $49,500 / 90 = $ 412.50 / day
Therefore, Contractor A charges $ 600 per day and contractor B charges $412.50 per day.
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Of the 180 days of school last year, Grace was absent 15 days. What percent of the day was she absent?
Suppose a family starts out 50 miles from home at time t = 0. They travel away from home at a constant speed of 45 miles an hour. What's the equation that tells you how far they'll be from home t hours later? (Assume d is distance in miles.) A. d = 45t + 50 B. d = 45t C. d = 50t D. d = 50t + 45
How does one find the equation y=ax²+bx+c when you are only provided with the coordinates of the turning point, (-6,-9)? Note: a is +1 or -1
What is the quotient? n+3/2n-6 divide n+3 /3n-9
A store advertises that it is offering a 14% discount on all articles purchased at the store. if yao pays $670.80 for an article, what was the marked price for the article?
Engineers must consider the breadths of male heads when designing motorcycle helmets. men have head breadths that are normally distributed with a mean of 6.0 in and a standard deviation of 1.0 in. (based on anthropometric survey data from gordon, churchill, et al.). if one male is randomly selected, find the probability that his head breadth is less than 6.2 in. use 4 decimals for your answer.
Answer: 0.9772 (the answer above wasn't the right one;)
Using z-score formula, the probability that a male's head breadth is less than 6.2 inches, would be approximately 57.9261%.
What is z-score formula?When you have multiple samples and want to describe the standard deviation of those sample means (the standard error), you would use this z score formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
This z-score will tell you how many standard errors there are between the sample mean and the population mean.
We have been given that men have head breadths that are normally distributed with a mean of 6.0 inches and a standard deviation of 1.0 inches. We are asked to find the probability that a man's breadth is less than 6.2 inches.
First of all, we will find z-score corresponding to sample score of 6.2 as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
where,
z = Z-score,
x = Sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
Upon substituting our given values in z-score formula, we will get:
[tex]z=\frac{6.2-6.0}{1.0}[/tex]
[tex]z=\frac{0.2}{1.0}[/tex]
z = 0.2
Now, we need to find the probability that a z-score is less than 0.2.
Using normal distribution table, we will get:
P(z < 0.2) = 0.57926
0.579261 ≈ 57.9261 %
Therefore, the probability that a male's head breadth is less than 6.2 inches, would be approximately 57.9261%.
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Sayed gave an answer of 6 6/7 for the problem 4 2/7 x 1 3/5. using estimates, is this a reasonable answer?
dividing mixed fractions
A gift box in the shape of a triangular prism has a volume of 36 cubic inches, a base height of 4 inches, and a height of 3 inches. What is the length of the base?
Answer:
6 inches is the base
Step-by-step explanation:
So you have to think back to what the formula to volume is. From there plug in numbers until you get your answer
In order to survive, organisms must maintain stable conditions in their bodies, even though their external environments are always changing.
For example, humans need to maintain an internal temperature around 37°C. Blood needs to have a pH around 7.4 and an oxygen saturation close to 100%.
What needs to happen in order to maintain these conditions?
A) Organ systems must interact with one another.
B) Organisms must be at rest.
C) Genes must be altered each time cells replicate.
D) All of these.
Organ systems must interact with one another.
Is 2 miles greater too 3,333 yards or is 3,333 yards greater than 2 miles?
What is the sum of the arithmetic series below? Use the formula for the sum of an arithmetic series.
Answer: The required sum is 504.
Step-by-step explanation: We are given to find the sum of the following arithmetic series using the formula for the sum of an arithmetic series :
[tex]\sum_{i=1}^{18}(2i+9).[/tex]
The given arithmetic series can be written, in expanded form, as follows :
[tex]11+13+15+17+~.~.~.~+43+45.[/tex]
We know that
the sum of first n terms of an arithmetic series with first term a and common difference d is given by
[tex]S=\dfrac{n}{2}\{2a+(n-1)d\}.[/tex]
In the given series, a = 11 and d = 13 - 11 = 15 - 13 = . . . =2.
Therefore, the sum up to 18 terms will be
[tex]S_{18}=\dfrac{18}{2}\{2\times 11+(18-1)\times2\}=9(22+34)=9\times56=504.[/tex]
Thus, the required sum is 504.
The sum of the arithmetic series ∑₁¹⁸(2i + 9) using the arithmetic series formula is 504.
To find what is the sum of the arithmetic series ∑₁¹⁸(2i + 9) below using the formula for the sum of an arithmetic series, we proceed as follows
The formula for the sum of therms of an arithmetic series is given by
Sₙ = n/2(a + Tₙ) where
n = number of termsa = first term and Tₙ = last termNow, since we have that arithmetic series, ∑₁¹⁸(2i + 9), the nth terms is U = 2i + 9
Now, the first term is when i = 1.
So, U₁ = a = 2(1) + 9
= 2 + 9
= 11
Also, the last term is when i = 18
So, U₁₈ = T₁₈ = 2(18) + 9
= 36 + 9
= 45
So, the sum of terms Sₙ is when n = 18
S₁₈ = 18/2(11 + 45)
= 9(56)
= 504
you have a large container of olive oil. You have used 22 1/2 quarts of oil. Twenty-five percent of the olive oil remains. How many quarts of olive oil remain?
Solution:
we are given that
You have a large container of olive oil. You have used [tex]22 \frac{1}{2}[/tex] quarts of oil.
Twenty-five percent of the olive oil remains.
we have been asked to find how many quarts of olive oil remain?
Let there were x quarts of olive oil.
It mean , we can write
[tex]x-22 \frac{1}{2}=\frac{1}{4}*x[/tex]
[tex]x-\frac{1}{4}*x=22 \frac{1}{2}[/tex]
[tex] \frac{3x}{4}=22 \frac{1}{2}[/tex]
[tex] 3x=4*22 \frac{1}{2}[/tex]
[tex] x=\frac{4}{3}* \frac{45}{2}[/tex]
[tex] x=30[/tex]
Hence quarts of olive oil remain [tex] =30-\frac{45}{2}=\frac{15}{2}=7\frac{1}{2}[/tex]
A map of Scotland is drawn to scale of 1:325,000.
how many CM on the map would show 65KM?
On a map of Scotland, drawn to the scale of 1:325,000, 65 KM of real-world distance will be represented by 20 cm on the map.
Explanation:The question pertains to the scale existing on a map. A map scale enables us to convert the measurements on the map into the corresponding real-world distances. Here, we have a map of Scotland that is drawn to the scale of 1:325,000. This signifies that 1 cm on the map equates to 325,000 cm in reality.
To ascertain how many cm on the map would represent 65 KM, we first need to convert 65 KM into cm. As we know, 1 KM is equal to 100,000 cm. Therefore, 65 KM will be equivalent to 65 * 100,000 = 6,500,000 cm.
Now, we divide the real-world cm (6,500,000 cm) by the scale (325,000), which gives us the cm on the map. Thus, 6,500,000 cm / 325,000 = 20 cm
So, on this map, 65 KM will be denoted by 20 cm.
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When ordering hot cocoa, Jackson is asked if he wants milk chocolate, dark chocolate, or chocolate mint flavor. He also must choose between a small or large mug, and has the option of adding marshmallows. How many ways can Jackson order his hot cocoa? A). 10
B).6
C).7
D).12
There are 12 ways Jackson can order his hot cocoa by choosing from three flavors, two mug sizes, and the option of adding marshmallows. Option D is correct,
To find the total number of ways Jackson can order his hot cocoa, we need to consider all the possible combinations of choices he has.
1. Flavor: Jackson has 3 options: milk chocolate, dark chocolate, or chocolate mint flavor.
2. Mug Size: Jackson has 2 options: small or large mug.
3. Marshmallows: Jackson has 2 options: with or without marshmallows.
To find the total number of combinations, we multiply the number of options for each choice:
[tex]\[ \text{Total combinations} = \text{Number of options for flavor} \times \text{Number of options for mug size} \times \text{Number of options for marshmallows} \]\[ \text{Total combinations} = 3 \times 2 \times 2 \]\[ \text{Total combinations} = 12 \][/tex]
So, there are 12 ways Jackson can order his hot cocoa. Therefore, the correct answer is option D) 12.
Steve opened a bank account.he plans to deposit $35 every month.write an equation that models the total amount of money,t,deposited after m months
Round 6 4/9 to nearest whole number
Two events, X and Y, are independent of each other. P(Y) = 5/6 and P(X and Y) = 1/3. What is P(X) written as a decimal? Round to the nearest tenth, if necessary.
Answer:option C
Step-by-step explanation: edge
The area of a trapezoid is found using the formula A=1/2h(b^1+b^2), where b^1 and b^2 are the parallel sides of the trapezoid and h is the height. The area of a trapezoid is 18km^2 , with bases 5 km and 7 km. What is the height, in
Answer:
40
Step-by-step explanation:
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A school sold small and large boxes of fruit for a fundraiser. One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218. Their sales can be represented in two equations where x represents the price of the small boxes and y represents the price of the large boxes. Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? Check all that apply.
1 The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.
2 The first equation can be multiplied by 5 and the second equation by 12 to eliminate x.
3 The first equation can be multiplied by –7 and the second equation by 13 to eliminate y.
4 The first equation can be multiplied by 7 and the second equation by –13 to eliminate y.
5 The first equation can be multiplied by 12 and the second equation by –5 to eliminate x.
6 The first equation can be multiplied by 7 and the second equation by 13 to eliminate y.
Answer:
A,C,D,E
Step-by-step explanation:
An equation is formed of two equal expressions. The correct options are 1, 3, 4, and 5.
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218. Also, x represents the price of the small boxes and y represents the price of the large boxes. Therefore,
The equation for the first student can be written as,
5x + 13y = 232
The equation for the second student can be written as,
12x + 7y = 218
Now, the multiplication that can be done to eliminate the variables are,
1.) The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.
3.) The first equation can be multiplied by –7 and the second equation by 13 to eliminate y.
4.) The first equation can be multiplied by 7 and the second equation by –13 to eliminate y.
5.) The first equation can be multiplied by 12 and the second equation by –5 to eliminate x.
Hence, the correct options are 1, 3, 4, and 5.
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What words can you use to read 14.895
Which is greater 9/8ths or 2 halves?
The correct answer is [tex]\frac{9}{8}[/tex] is greater than 2 halves.
To compare 9/8ths and 2 halves, we need to convert them to equivalent fractions with the same denominator, and then compare their numerators.
[tex]\text{Step 1: Convert 2 halves to an equivalent fraction with the denominator of 8}[/tex]
[tex]2\text{ halves} = 2 \times \left(\frac{4}{8}\right) = \frac{8}{8}[/tex]
[tex]\text{Step 2: Compare the numerators of }\frac{9}{8}\text{ and }\frac{8}{8}[/tex]
[tex]\text{Since }9 > 8\text{, therefore, }\frac{9}{8} > \frac{8}{8}[/tex]
Therefore, [tex]\frac{9}{8}[/tex] is greater than 2 halves.
6 surfaces 2 small stand tall what shape
Which sum is equal to 7/12?
A. 1/12 + 1/12 + 1/12 +1/12 + 1/12 + 1/12 +1/12
B. 1/7 + 1/7 + 1/7 +1/7 +1/7 + 1/7 + 1/7
C. 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12
D. 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 +
Answer:
The answer is A.
Step-by-step explanation:
There are 7 1/12ths, so it is equal to 7/12
A pizza parlor uses square prisms for their pizza boxes. Due to the crust rising, the height of their boxes is always 2 inches. Additionally, the volume of the pizza box must be 450 cubic inches to fit their standard-sized pizza. A worker determined that the equation below could be used to find the side length, x, of the box needed to reach that volume.
Answer:
The solutions are -15 and 15, but only 15 is a reasonable side length.
Step-by-step explanation:
Got it right on the test.
Luca has a box of dog toys. There are 3 bones, 5 balls, and a stuffed animal. What is the ratio of balls to stuffed animals?
Answer:
5.1
Step-by-step explanation:
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Write two equivalent fractions for 2/3
5 hours 8 min - 3 hours 12 min