Answer: 7.8
Step-by-step explanation:
Evaluate the expression 5^x- 3^x5 x −3 x 5, start superscript, x, end superscript, minus, 3, start superscript, x, end superscript for x=2x=2x, equals, 2.
Question:
Evaluate the expression 5^x - 3^x for x=2
Answer:
5^x - 3^x for x=2 is 16
Step-by-step explanation:
Given
5^x - 3^x
x=2
Required
Evaluate
When fazed with question like this all you need is to substitute the value of x (or any other variable{s} used) in the expression.
Recall that x = 2
So, you have to substitute 2 for x in 5^x - 3^x
This gives
[tex]5^2 - 3^2[/tex]
This can be further solved in 2 ways
1. Solve directly
[tex]5^2 - 3^2[/tex]
= [tex]25 - 9[/tex]
= 16
2. Expand using difference of two squares.
Difference of two squares is represented by
[tex]a^2 - b^2 = (a + b) (a - b)[/tex]
By comparison
[tex]5^2 - 3^2[/tex] becomes
[tex]5^2 - 3^2 = (5 + 3) (5 - 3)[/tex]
[tex]5^2 - 3^2 = (8) (2)[/tex]
[tex]5^2 - 3^2 = 8 * 2[/tex]
[tex]5^2 - 3^2 = 16[/tex]
For both ways, we'll arrive at the same answer.
Hence, 5^x - 3^x for x=2 is 16
Answer:
5^x - 3^x for x=2 is 16
Step-by-step explanation:
The rectangle is 20 by 16 and the scale factor is 0.25. What are the dimensions of the reduced rectangle?
Answer:
5 by 4
Step-by-step explanation:
0.25 x 20 = 5
0.25 x 16 = 4
Answer:
5 y 4
Step-by-step explanation:
I had this qweston.
Help me plz plz plz :(
Here is a right angled triangle
Answer:
10
Step-by-step explanation:
cos60=0.5
cos60= 5/x hence x=5÷cos60(0.5)
=5÷0.5=10
the third segment in the graph is not as step as the segment. what does this mean?
in geometry a line segment part of a line that is bounded by two distinct endpoints
The perimeter of a rectangle is 68 cm. The length is 4 cm more than its
width. Find the length of the rectangle.
Answer:
21
Step-by-step explanation:
68 divided by 4 sides is 17 subtract 4 cm for width and add 4 cm for length to get 21 cm for length and 13 cm for width
Martha made 3 birthday cards, and she wants to make more. If she makes 5 cards an hour, how many cards will she have after 6 hours? REMEMBER TO ADD THE ORIGINAL 3 TO THE NUMBER SHE MAKES IN 6 HOURS. ANSWER WITHOUT UNITS.
Answer:
33
Step-by-step explanation:
just multiply 5*6 and add three to the result
Answer:
33
Step-by-step explanation:
Every hour she makes 5 cards, and she makes them for 6 hours so you need to multiply 6 with 5 to get 30, then add up the 3 she made earlier...33 :D
Mike bought 7 new baseball cards to add to his collection. The next day his dog ate half of his collection. There are now only 41 cards left. How many cards did Mike start with?
Answer: Mike started with 75 cards
Step-by-step explanation:
Hi, to answer this question we have to write an equation:
The number of cards mike started with (x) plus the new cards added (7) must be divided by 2 (since his dog ate half of his collection).
That expression must be equal to the number of cards left (41)
Mathematically speaking:
(x + 7) /2 = 41
Solving for x:
x+7 = 41x2
x+7 = 82
x = 82-7
x = 75 cards
Feel free to ask for more if needed or if you did not understand something.
What decimal part of 60 is 45?
Answer:
0.75
Step-by-step explanation:
45 is three-fourths of sixty
three fourths as a fraction is .75
hope this helps!!!
Answer:
0.75
Step-by-step explanation:
you divide 45 by 60 and you will get 0.75
A rectangle has a length of 4 inches and area of 12 in.² what is the perimeter of the rectangle
Answer:
14 in
Step-by-step explanation:
breadth = 12/4 = 3
perimeter = 3+3+4+4 = 14
How do we write 1/5 as a decimal?
Answer:
1/5 as a decimal is written as 0.2
Answer:
This makes you get 0.2So you have the fraction 15 . What the divided sign is, is basically just a division sign. So, to get the decimal, you do 1÷5 .
Step-by-step explanation:
So you have the fraction 15 . What the divided sign is, is basically just a division sign. So, to get the decimal, you do 1÷5 .
Find the mean and the mean average height.
Answer:
a.) [tex]mean=200.3[/tex]
b.) [tex]210[/tex] [tex]cm[/tex]
Step-by-step explanation:
a.) We are given the heights and their frequency. We can make a new set:
198, 199, 199, 199, 200, 200, 201, 201, 201, 201, 201, 202, 202
Now find the mean. The mean is found by adding all the numbers in the set, then dividing the total by the number of terms in the set. Add:
[tex]198+199+199+199+200+200+201+201+201+201+201+202+202=2604[/tex]
Now count the terms. There are 13 terms. Divide the total by the number of terms:
[tex]\frac{2604}{13}= 200.3[/tex]
The mean is 200.3.
b.) Use random values like 200, 198 etc. and add them to the total of the last set, then divide by 14 instead of 13 (because there is a new player). Do this until you get a mean of 201 with the new height:
[tex]2604+210=2814\\\\\frac{2814}{14}= 201[/tex]
For the new mean to be 201 cm, the new player has a height of 210 cm.
Finito.
To estimate the mean height of students at your college or university with 93 percent confidence and a margin of error of 1 inch, you would need to measure approximately 333 male students.
Explanation:To estimate the mean height of students at your college or university with 93 percent confidence and a margin of error of 1 inch, you need to use the formula for sample size.
The formula for sample size is:
N = ((Z * σ) / E)^2
Where N is the sample size, Z is the Z-score for the desired confidence level, σ is the standard deviation, and E is the margin of error.
In this case, the Z-score for 93 percent confidence is 1.8119 (found using a Z-table). The standard deviation is given as 2.5 inches. Substituting these values into the formula:
N = ((1.8119 * 2.5) / 1)^2
N = 18.2255^2
N ≈ 332.3782
Rounding up to the nearest whole number, you would need to measure approximately 333 male students to estimate the mean height with 93 percent confidence and a margin of error of 1 inch.
Lena tried to solve a system of linear equations algebraically and in process found the equation 5=9. Lena thought something was wrong,so she graphed the equations and found that they were parallel lines. Explain whats Lenas graph and equation could mean.
Answer:
This means that there is no solution
Step-by-step explanation:
When solving for a system of linear equations, we are solving for the intersection point. If we cannot algebraically solve for a system, it automatically means you made a mistake or the lines are parallel. Since the two lines are parallel, there is no intersection point, so there is no solution
Which situation can be modeled by the inequality 3+7<13?
The inequality 3+7<13 represents a situation where the sum of three units and seven units is less than thirteen units. While this does not hold true in a strict mathematical sense, it illustrates the notion of inequality.
Explanation:The inequality 3+7<13 represents a situation where the sum of three units and seven units is less than thirteen units. The numbers could represent any sorts of units, depending on the real-world situation.
For instance, let's consider an example where each unit represents one apple. According to this inequality, if you have three apples and you add seven more apples, the total number of apples you have would be less than thirteen. As you can see, this does not make sense, because 3+7 equals 10, which is not less than 13. Thus, the inequality 3+7<13 does not hold true in this situation.
This example illustrates that the given inequality does not hold true in a mathematical sense because 3 + 7 equals 10, which is not less than 13. However, in a situation where there is a numerical error or logical inconsistency, this inequality could potentially be used.
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Dwayne buys ingredients to make a cake. He buys 112 pounds of flour, 12 ounces of coconut, and 114 pounds of sugar. What is the total weight of the ingredients Dwayne bought? Select all that apply. A. 56 ounces B. 3 pounds 8 ounces C. 13 3/ 4pounds D. 13 3/ 4ounces E. 3 1/2pounds
Answer:
The only correct options are A, B and E.
Step-by-step explanation:
He buys [tex]1\frac{1}{2}[/tex] pounds of flour, 12 ounces of coconut, and [tex]1\frac{1}{4}[/tex] pounds of sugar.
We will add these together, but before that, we convert the 12 ounces to pounds, so that all the units are the same:
1 ounce = 0.0625 pounds
12 ounces = 12 * 0.0625 = [tex]\frac{3}{4}[/tex] pounds
He buys [tex]\frac{3}{4}[/tex] pounds of coconut.
Adding all of them together yields:
[tex]1\frac{1}{2}[/tex] + [tex]\frac{3}{4}[/tex] + [tex]1\frac{1}{4}[/tex] = [tex]3\frac{1}{2}[/tex] pounds
Let us also convert to ounces:
[tex]3\frac{1}{2}[/tex] / 0.0625 = 56 ounces
Let us also convert 1/2 pound to ounces:
1/2 / 0.0625 = 8 ounces
Hence, the total weight of ingredients that Dwayne bought is [tex]3\frac{1}{2}[/tex] pounds or 56 ounces or 3 pounds 8 ounces
Hence, options A, B and E are correct.
An expression is shown. 3/5÷5/8 What is the value of the expression?
Answer:
24/25
Step-by-step explanation:
3/5×8/5
24/25
An elevator started on the 10th floor of a large hospital. it traveled up 4 floors, then down 6 floors, then down 2 more floors, and finally went back up 7 floors. Which floor was the elevator on when it stopped?
After a series of movements starting on the 10th floor, the elevator stopped on the 13th floor.
To determine which floor the elevator was on when it stopped, we need to perform a series of additions and subtractions based on the elevator's movements, as described:
The elevator started on the 10th floor.
It traveled up 4 floors: 10 + 4 = 14th floor.
Then down 6 floors: 14 - 6 = 8th floor.
Then down 2 more floors: 8 - 2 = 6th floor.
Finally, it went back up 7 floors: 6 + 7 = 13th floor.
After completing all these movements, the elevator stopped on the 13th floor.
The product of two consecutive integers is 72. The equation x(x + 1) = 72 represents the situation, where x
represents the smaller integer. Which equation can be factored and solved for the smaller integer?
x2 + x - 72 = 0
O2 + x + 72 = 0
x2 + 2x - 72 = 0
2 + 2x + 72 = 0
Answer:
x^2+x-72=0
Step-by-step explanation:
Hope this helps!
Answer:
x^2+x-72=0
Step-by-step explanation:
Find the measure of b
Ethan Purchased a gently used minivan 2 years ago. the current value of the van is $8000 the vans value depreciated by 11% each year. how much does Ethan pay for the van?
Answer:
18,736.80
Step-by-step explanation:
Final answer:
To determine the original purchase price of the van, we apply the formula for exponential decay and find that Ethan paid approximately $10,100.45 for the van two years ago, taking into account a depreciation rate of 11% per year.
Explanation:
To find how much Ethan paid for the van, we need to work backwards from the current value and consider the annual depreciation rate.
To do this, we can use the formula for exponential decay which is final value = initial value × (1 - rate of depreciation)number of years. Given the final value ($8000) and the depreciation rate (11% or 0.11), we need to solve for the initial value, which represents the price Ethan paid for the van.
Let's set up the equation:
8000 = initial value × (1 - 0.11)2
8000 = initial value × (0.89)2
8000 = initial value × 0.7921
Initial value = 8000 / 0.7921
Initial value ≈ $10,100.45
Therefore, Ethan paid approximately $10,100.45 for the van.
after making 20 servings of pasta, a chef has used 30 cloves of garlic. how many cloves are used to make 10 servings?
Answer:
15
Step-by-step explanation:
I'm not the brightest, mind helping me out?
Answer:
C.
Step-by-step explanation:
Opposite means that they are the same value away from 0 just on the opposite side.
4 is opposite to -4
and 7 is opposite to -7
The radius of a circle is 8.6 centimeters.
Enter the area of the circle, in square centimeters. Round your answer to the nearest hundredth and use 3.14 for pi.
______ square centimeters
Answer:
8.6 x 3.14 = 27.00cm (squared) I think. Double check that. But i think ( .00 ) is in the hundredths.
Final answer:
The area of a circle with a radius of 8.6 centimeters is approximately 232.23 square centimeters when calculated using 3.14 for Pi and rounding to the nearest hundredth.
Explanation:
The question is asking to find the area of a circle with a given radius. The formula to calculate the area of a circle is A = πr², where π is a constant (Pi, approximately 3.14) and r is the radius of the circle. To calculate the area with the given radius of 8.6 centimeters:
Insert the radius into the area formula: A = π × (8.6 cm)²
Perform the squaring of the radius: 8.6 cm × 8.6 cm = 73.96 cm²
Multiply the result by Pi (using 3.14 for π): A = 3.14 × 73.96 cm²
Calculate the product: A = 232.23 cm²
Round the result to the nearest hundredth: A ≈ 232.23 cm²
Therefore, the area of the circle is approximately 232.23 square centimeters.
A regulation basketball hoop has a rim with an 18-inch diameter. What is the approximate length around the rim of a regulation basketball hoop?
Answer:
Step-by-step explanation:
The circumference of a regulation basketball hoop with an 18-inch diameter is approximately 56.52 inches.
The question asks for the approximate length around the rim of a regulation basketball hoop, which has an 18-inch diameter. To find the circumference (the length around the rim), we can use the formula:
Circumference =
pi imes diameter
Since the diameter of the rim is 18 inches, we can approximate
pi as 3.14 to calculate the circumference:
Circumference = 3.14 imes 18 inches = 56.52 inches
Thus, the approximate length around the rim of a regulation basketball hoop is about 56.52 inches.
Which describes all of the values for which the graph is
positive and decreasing?
O all real values of x where x<-1
O all real values of x where x < 1
O all real values of x where 1
O all real values of x where x > 3
Answer: C
Step-by-step explanation:
I went w/ my trusty C and got it right on e2020
All real values of x where 1 < x < 3. Therefore, option C is the correct answer.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
The positive regions of a function are those intervals where the function is above the x-axis.
It is where the y-values are positive (not zero).
Therefore, option C is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Which describes all of the values for which the graph is positive and decreasing?
A.all real values of x where x < −1
B.all real values of x where x < 1
C.all real values of x where 1 < x < 3
D.all real values of x where x > 3
The percentage profit on an MP3 player purchased for $320 and later sold for $350 is
Answer:
The profit percentage in MP3 player is 9.37 %.
Step-by-step explanation:
Cost price of MP3 player is $320
Selling price of MP3 player is $350.
Here, selling price is more than cost price. It means there is profit in MP3 player.
Profit = SP - CP
Profit = 350 - 320
Profit = $30
Profit percentage is given by :
[tex]\% P =\dfrac{{SP}-{CP}}{{CP}}\times 100\\\\\% P=\dfrac{30}{{320}}\times 100\\\\\% P=9.37\%[/tex]
The profit percentage in MP3 player is 9.37 %.
Need help now please answer
Answer:
10 cm
Step-by-step explanation:
We want to find TS = ST
ST = CD from the second statement of congruence
CD = IJ from the first statement of congruence
We know IJ = 10
That means ST = 10
Phan earned gross wages of $487.12. Phan's deductions were: $49 in federal withholding taxes, 6.2% in social security taxes, 1.45% in Medicare taxes, $28.74 in health insurance, and $12 in union dues. Find Phan's net pay.
Answer:
$360.12
Step-by-step explanation:
Phan's net pay would be equal to the gross wage he receives minus the deductions:
Gross wage= $487.12
Federal withholding taxes= $49
Social security taxes= $487.12*6.2%= $30.2
Medicare taxes= $487.12*1.45%= $7.06
Health insurance= $28.74
Union dues= $12
Net pay= $487.12-$49-$30.2-$7.06-$28.74-$12
Net pay= $360.12
According to this, Phan's net pay is $360.12.
Phan's net pay is calculated by subtracting the sum of Social Security tax, Medicare tax, federal withholding, health insurance, and union dues from his gross wages. After performing the calculations, Phan's net pay is $360.12.
To calculate Phan's net pay, we first need to determine the amount of each deduction from his gross wages. We will follow these steps:
Calculate the Social Security tax: 6.2% of $487.12.Calculate the Medicare tax: 1.45% of $487.12.Add the fixed deductions: federal withholding taxes, health insurance, and union dues.Subtract the total of all deductions from the gross wages to find the net pay.Now let's do the math:
Social Security tax = 6.2% of $487.12 = $30.20Medicare tax = 1.45% of $487.12 = $7.06Total fixed deductions = $49 (federal withholding) + $28.74 (health insurance) + $12 (union dues) = $89.74Adding up all the deductions: $30.20 (Social Security) + $7.06 (Medicare) + $89.74 (fixed deductions) = $127.To calculate the net pay:
Gross wages = $487.12
Total deductions = $127.00
Net pay = Gross wages - Total deductions
Net pay = $487.12 - $127.00 = $360.12
Therefore, Phan's net pay is $360.12.
Kate had 70 brooms; Alisa had 20 more brooms than Kate. What was the ratio of Kate’s brooms to Alisa’s brooms?
Answer:
7:9
Step-by-step explanation:
it was 70:70+90 cuz it was 20 moe than kates broom and if u simpifly that it will be 7:9 and sorry if my grammers bad im also a student lol i hope this helps. :)
Given that Kate possessed 70 brooms and Alisa had 20 more brooms than her, Alisa possessed 90 brooms. The ratio of Kate's brooms to Alisa's brooms reduces to 7:9.
Explanation:The question wants to find the ratio of brooms Kate has to the brooms Alisa has. Firstly, we know Kate has 70 brooms. The question also tells us that Alisa has 20 more brooms than Kate, which means Alisa has 70+20=90 brooms. To establish a ratio, we simply put Kate's brooms to Alisa's brooms which gives us 70:90. However, we always want to reduce the ratio to its simplest form. Both 70 and 90 are divisible by 10, so we divide each side by 10, getting 7:9. The ratio of Kate's brooms to Alisa's brooms is therefore 7:9.
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What the answer to this
Answer:
(4, -15) is the vertex, a
Step-by-step explanation:
y=x^2-8x+1
-b/2a=x
y = ax^2 + bx + c
a=1 b=-8 c=1
x=8/2(1)
x=8/2
4 is the x of the vertex
y=4^2-8(4)+1
y=16-32+1
y=-15
(4, -15)
Hope this helps! Please mark brainliest :)
Answer: A (4,-15)
Step-by-step explanation:
Two similar pyramids have base areas of 122 cm? and 16 cm? The surface area of the larger pyramid is 56 cm
What is the surface area of the smaller pyramid?
40.1 cm
42.7 cm
522 cm
59.8 cm
Answer:
42.7 cm sq.
Step-by-step explanation:
small/large = 16 / 122
16/122 = S / 56
S = 56 * (16/122) = 7.34...
however not in the choice
ah ha..
You meant : 12.2 sq. cm : 16 sq. cm = small / large
so 12.2 / 16 = S / 56 cm
S = 42.7 sq. cm
The surface area of the smaller pyramid is approximately 42.7 cm. Answer: B) 42.7 cm
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
If two pyramids are similar, their corresponding linear dimensions (height, slant height, etc.) are in the same ratio as their corresponding base dimensions.
Let the height of the larger pyramid be h, and let the height of the smaller pyramid be x, h, where x is the scaling factor.
The ratio of their base areas is given by:
(xh)² : h² = 16 : 122
Simplifying this equation, we get:
x²h² = 16/122 * h²
x² = 16/122
x = √(16/122)
Now we know that the linear dimensions of the smaller pyramid are
1/√(122/16) = √(16/122) times that of the larger pyramid.
So, the surface area of the smaller pyramid is:
(16/122) * (56 / (√(16/122))²) = 42.7 cm (rounded to one decimal place)
Therefore, the surface area of the smaller pyramid is approximately 42.7 cm. Answer: B) 42.7 cm
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