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If (7^2)x = 1, what is the value of x? Explain your answer.
If (7^0)x = 1, what are the possible values of x? Explain your answer.
(7^2)x = 1
7^2 = 49
49x = 1
x = 1/49
(7^0)x=1
7^0 = 1 (anything raised to 0 = 1)
1x = 1
x = 1
Which second-degree polynomial function has a leading coefficient of 3 and roots –4 and 6?
The sum of three consecutive integers is 90. Find the integers
The sum of three consecutive integers is 90. So you know that 3 numbers that are next to each other in numerical order equals 90.
First step: Make an equation:
Let's take x as the smallest of the three numbers.
[tex]x +(x+1)+(x+2)=90[/tex]
2nd step: Open the brackets:
[tex]x+x+1+x+2=90[/tex]
3rd step: Simplify:
[tex]3x+3=90[/tex]
4th step: Keep similar integers on one side of the equation
[tex]3x+3-3=90-3[/tex]
5th step: Solve for x:
[tex]3x=87[/tex]
[tex]\frac{3x}{3} =\frac{87}{3}[/tex]
[tex]x=29[/tex]
So if the numbers are consecutive, they have to be next to each other.
Answer: 29, 30, 31
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Help with #30 Please!
The perimeter of a rectangular house is 122 ft. the width is 5 ft less than the length. find the length and the width.
After a discount of 10%, the price of a pair of jeans, including tax, was $69.62. The following equation can be used to find x, the price of the pair of jeans without the discount:
x - 0.1x + 0.07(x - 0.1x) = 69.62
What is the price of the pair of jeans without the discount?
A-$70.58
b-$72.29
c-$74.86
d-
What point in the feasible region maximizes the objective function constraints: x>=0 y>=0 -x+3>=y y<=1/3 x+1 Objective function: C=5x-4y Please explain!
Answer:
So, the maximum of C is 15 at (3,0) and the minimum value is 0 at (0,0)
Step-by-step explanation:
When you graph all of the constraint functions, the vertices of the shape that is made are at the points above. Now you plug those points into the function equation C=5x-4y and see where you get a max or min.
(0,1)
(1.5,1.5)
(0,0)
(3,0)
(1,1)=C=1
(1.5,1.5)=C=1.5
(0,0)=C=0
(3,0)=C=15
So, the maximum of C is 15 at (3,0) and the minimum value is 0 at (0,0)
Kareem runs 6 miles in 55 minutes. At the same rate, how many miles would he run in 44 minutes?
69.5 is What precent of 85?
Sara bought two pounds of strawberries for $5.12. What is price in dollars per ounce of strawberries 1 pound =16 ounces
what percent of 176 is 17.6
What is 2r+7+r=? I'm not sure
What is the general term equation, an, for the arithmetic sequence 5, 1, −3, −7, . . . , and what is the 21st term of this sequence?
Write the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1).
A) y + 6 = -1(x – 5)
B) y – 6 = -1(x + 5)
C) y + 6 = 1(x – 5)
D) y – 6 = 1(x + 5)
The point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1) is [tex]\( \boxed{A) y + 6 = -1(x - 5)} \)[/tex].
To find the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1), we first need to calculate the slope (m) using the formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given points:
[tex]\((-5, 6)\) and \((0, 1)\)[/tex]
Calculate the slope m:
[tex]\[ m = \frac{1 - 6}{0 - (-5)} = \frac{-5}{5} = -1 \][/tex]
Now that we have the slope m = -1, we can use the point-slope form of the equation of a line, which is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Choose one of the points, let's use [tex]\((-5, 6)\) as \((x_1, y_1)\)[/tex]:
[tex]\[ y - 6 = -1(x + 5) \][/tex]
Now, simplify and compare with the given options:
[tex]\[ y - 6 = -1(x + 5) \][/tex]
So, the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1) is [tex]\( \boxed{A) y + 6 = -1(x - 5)} \)[/tex].
you earn $70 per week mowing lawns one week you work 10 hours during the week and spend $20 on gasoline for your mower how much do you earn each hour
22 less than 5 times a number f into a algebraic expression
What is factor out the coefficient of the variable of 4h-3
Write 0.0004571 in scientific notation.
An airline, believing that 4% of passengers fail to show for flights, overbooks (sells more tickets than there are seats). suppose that for a particular flight involving a jumbo-jet with 267 seats, the airline sells 276 tickets.
a. what is the expected number of ticket holders that will fail to show for the flight?
The expected number of ticket holders that will fail to show for the flight is 11.
Given that,
There is a fail percentage of 4%.There are 267 seats.And, the 276 airline tickets are sold.Based on the above information,
= 276%
= 2.76
Now the number of ticket holders who fail for presenting the flight should be
[tex]= 2.76\times 4[/tex]
= 11
Therefore we can conclude that the expected number of ticket holders that will fail to show for the flight is 11.
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Birth weights of babies born to full-term pregnancies followed roughly a normal distribution. at meadowbrook hospital, the mean weight of babies born to full-term pregnancies is 7 pounds with a standard deviation of 14 ounces (1 pound = 16 ounces). what is the probability that the average weight of the four babies will be more than 7.5 pounds
To find the probability that the average weight of four babies will be more than 7.5 pounds, we calculate the z-score and look it up in the standard normal distribution table. The probability is approximately 0.2843, or 28.43%.
Explanation:To find the probability that the average weight of four babies will be more than 7.5 pounds, we need to calculate the z-score and look it up in the standard normal distribution table.
First, we convert the weight of 7.5 pounds to ounces: 7.5 pounds * 16 ounces = 120 ounces.
Next, we calculate the z-score using the formula: z = (x - &μ) / &σ, where x is the given weight, &μ is the mean weight, and &σ is the standard deviation. In this case, z = (120 - 112) / 14 = 0.571.
Finally, we can look up the probability using the z-score in the standard normal distribution table. The probability of the average weight of four babies being more than 7.5 pounds is approximately 0.2843, or 28.43%.
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The sum of any two consecutive prime numbers is also prime
how do you factor 30n^2b-87nb+30b?
Lydia purchased a 15 cup bag of pasta. the suggested serving is 3/4 cup per person. how many servings are in a 15 cup bag of pasta
To find out how many servings are in a 15 cup bag of pasta when serving size is 3/4 cup per person, divide 15 by 3/4, which equals 20 servings.
Firstly, convert the mixed fraction into an improper fraction for easier division: 3/4 remains the same since it is already a proper fraction.
Now, carry out the division: 15 ÷ (3/4)
= 15 × (4/3) (You multiply by the reciprocal of 3/4)
Then, multiply the numbers:
= 15 × 4 ÷ 3
= 60 ÷ 3
= 20
Therefore, there are 20 servings in a 15 cup bag of pasta when the serving size is 3/4 cup per person.
there are 182 seats in a theater. The seats are evenly divided into 13 rows. How many seats are in each row
Justin is exchanging dollars for rolls of quarters and rolls of dimes at a bank. Each roll of quarters has a value of $10 and each roll of dimes has a value of $5. He exchanges $90 and receives 11 rolls of coins. How many of each type of roll of coins did he receive?
6 rolls of dimes = $30.
6 rolls of quarters = $60.
Answer:
7 roll of quarter and 4 roll of dimes.
Step-by-step explanation:
Let x be the number of rolls of quarters and y be the number of rolls of dimes,
Given,
Total rolls = 11
⇒ x + y = 11 ------(1),
Also, the total value of $ 90 in which Each roll of quarters has a value of $10 and each roll of dimes has a value of $5.
⇒ 10x + 5y = 90 ------(2),
Equation (2) - 5 × Equation (1),
We get,
5x = 90 - 55
⇒ 5x = 35 ⇒ x = 7
From equation (1),
7 + y = 11 ⇒ y = 4
Hence, the number of roll of quarters = 7,
And, the number of roll of dimes = 4
The surface area of an open-top box with length L, width W, and height H can be found using the formula: A= 2LH + 2WH + LW Find the surface area of an open-top box with length of 7 cm, width 6 cm, and height 3 cm.
Final answer:
The surface area of an open-top box with a length of 7 cm, width of 6 cm, and height of 3 cm is calculated using the formula and comes out to be 120 cm².
Explanation:
To find the surface area of an open-top box with given dimensions, we use the formula: A= 2LH + 2WH + LW. Substituting in the provided lengths for length (L), width (W), and height (H):
A = 2(7 cm)(3 cm) + 2(6 cm)(3 cm) + (7 cm)(6 cm)
A = 2(21 cm²) + 2(18 cm²) + 42 cm²
A = 42 cm² + 36 cm² + 42 cm²
A = 120 cm²
This gives us the total surface area of the open-top box which is 120 cm².
Given that the restaurant is located in a city with a population over 500,000, what is the probability that it is in the northeast?
The probability is 0.187 or 18.7% that the restaurant chosen at random is in the north east and is located in a city with a population over 500,000.
To find the likelihood that a haphazardly picked eatery from the 588 outlets situated in a city with a populace more than 500,000 is in the north east, we really want to know the quantity of cafés that meet these two rules and are situated in the north east.
Let's look for this information using the table:
Northeast Midwest South West More than 500,000 Over 500,000 110 95 178 66 Less than 500,000 53 39 38 9 The table indicates that 110 restaurants are located in the north east of the United States in cities with more than 500,000 residents. In this manner, the likelihood that a haphazardly picked eatery from the 588 outlets situated in a city with a populace more than 500,000 is in the north east is:
P(Northeast and North of 500,000) = 110/588 = 0.187
Thus, the likelihood is 0.187 or 18.7% that the café picked aimlessly is in the north east and is situated in a city with a populace more than 500,000.
Hello, I am taking Quantitative methods for business, which has a lot of excel based mathematics and I was wondering if anyone could help. Here is the question:
Refer to the table that illustrates customer’s complaints about a manufacturing company.
A. What is the probability a customer complained during the guarantee period?
B. What is the probability that a customer complained about an electrical problem or a mechanical problem?
Table is included in attachment. Also Thank you!!!
The number of bacteria (b) in a batch of refrigerated food is given by the function b(t) = 20t2 − 70t + 300, where t is the temperature of the food in degrees Fahrenheit. The function t(h) = 2h + 3 gives the temperature of the food h hours after it is removed from refrigeration. Which expression correctly represents the number of bacteria (b) in the food as a function of the number of hours (h) the food is unrefrigerated?
During the 2008-2009 season,there were 801,372 people who attended the home hockey games in Philadelphia.There were 609,907 people who attended the home hockey games in Phoenix. How much greater was the home attendance in Philadelphia than in Philadelphia than in Phoenix that season?