Betsy is incorrect as he wrote [tex]3^4[/tex] = 12 but it should be 81.
What is Exponents and Power?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.
Given:
Expression: (8 + 18) x [tex]3^4[/tex]
Now, solving the Above Expression
(8 + 18) x [tex]3^4[/tex]
= 26 x [tex]3^4[/tex]
= 26 x ( 3.3.3.3)
= 26 x 81
= 2106
Betsy make a mistake as he wrote [tex]3^4[/tex] = 12 but it should be 81.
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In ΔNOP, the measure of ∠P=90°, the measure of ∠N=15°, and PN = 18 feet. Find the length of OP to the nearest tenth of a foot.
Answer:
4.8
Step-by-step explanation:
Which is the graph of y=2/(x+1)-6
Answer:
A on EDGE2020
The graph of the rectangular hyperbola that has the equation of the horizontal asymptote of y = -6 and the vertical asymptote of x = -1 will be drawn below.
What is the rectangular hyperbola?The asymptotes or axes of a rectangular hyperbola are parallel to one another. The conjugate axis and transverse axes have lengths that are identical.
An asymptote is a line that constantly reaches a given curve but does not touch at an infinite distance.
The rectangular hyperbola is shifted below. Then the horizontal also gets shifted below by 6 units. Then the equation of the horizontal asymptote is given as,
y = - 6
Then the equation of the vertical asymptote is given as,
x + 1 = 0
x = - 1
The graph of the rectangular hyperbola that has the equation of the horizontal asymptote of y = -6 and the vertical asymptote of x = -1 will be drawn below.
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On a certain hot summer's day, 744 people used the public swimming pool. The daily prices are $ 1.75 for children and $ 2.00 for adults. The receipts for admission totaled $ 1392.25 .How many children and how many adults swam at the public pool that day?
Answer:
383 children and 361 adults
Step-by-step explanation:
Let's say there are a adults and c children. Since the total number of people was 744, we can write:
a + c = 744
We also know that children's prices are $1.75 per child and adults' prices are $2 per adult. Since the total is $1392.25, we can write:
1.75c + 2a = 1392.25
Now we have a system of linear equations:
a + c = 744
1.75c + 2a = 1392.25
Multiply the first equation by 2:
2 * (a + c = 744) ⇒ 2a + 2c = 1488
Now subtract the second equation from this one:
2a + 2c = 1488
- 2a + 1.75c = 1392.25
___________________
0a + 0.25c = 95.75
c = 383
Plug this in to find a:
a + c = 744
a + 383 = 744
a = 361
There were 383 children and 361 adults.
Lets use some variables:
x = number of adults
y = number of children
744 total people used the public swimming pool and the number adults and children are unknown, so, we can write an equation like:
x + y = 744
Since $2 are for adults, we can write that as 2x. Since $1.75 are for children, we can write that as 1.75y. Since the total price is $1,392.25, that's what the equation should equal. Equation:
2x + 1.75y = 1,392.25
Now, we have a system of equations.
~Rationalize equations
x + y = 744, 2x + 7/4y = 5569/4
~Isolate x for [ x + y = 744 ]
x + y - y = 744 - y
x = 744 - y
~Substitute with x
2(744 - y) + 7/4y = 5569/4
~Isolate y for [ 2(744 - y) + 7/4y = 5569/4 ]
2(744 - y) * 4 + 7/4y * 4 = 5569/4 * 4
8(744 - y) + 7y = 5569
5952 - 8y + 7y = 5569
5952 - y = 5569
5952 - 5952 - y = 5569 - 5952
-y = -383
-y/-1 = -383/-1
y = 383
~Substitute y with 383 in [ x = 744 - y ]
x = 744 - 383
x = 361
Therefore, there are 361 adults and 383 children.
Best of Luck!
a concrete pillar has the shape of a cylinder. it has a diameter of 6 meters and a height of 7 meters. concrete cost $116 per cubic meter how much did the concrete cost for the pillar
Answer:
The cost of the pillar is $22,947.12
Step-by-step explanation:
Diameter of the pillar = 6m
Radius = diameter / 2 = 6 / 2 = 3m
Height if the pillar = 7m
Volume of the pillar = πr²h
π = 3.14
V = 3.14 × 3² × 7
V = 3.14 × 9 × 7
V = 197.82m³
Volume of the pillar is 197.82m³
If 1m³ = $116
197.82m³ will cost $x
X = (197.82 × 116) / 1
X = $22,947.12
The cost of the pillar is $22,947.12
ASAP!!!!10 Points!!!!!
Which describes the correlation show in the scatter plot?
There is a positive linear correlation
There is a negative linear correlation,
There is no positive or negative correlation
There is a nonlinear correlation
The correlation show in the scatter plot There is no positive or negative correlation
What is Correlation?A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical technique for describing straightforward connections without explicitly stating cause and consequence.
Given:
The positive linear correlation shows a line which is Diagonally rising.
and, The negative linear correlation shows a line which is Diagonally falling.
So, the graph we have no Correlation because it does not any falling and rising line.
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The front face of a cube has side lengths of 15 feet. It is related to the face of a larger cube by a scale factor of 1.8. What are the side lengths of the larger cube?
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i only know how to edit how do i delete answers this
isnt
what i wanna dooooooooo
sorry
The vertex of the parabola below is at the point (5,-3). Which of the equations
below could be the one for this parabola?
M
10-1
MC
10
(5.-3)
10
A. X = 3(y + 3)2 + 5
B. x = 3(y - 5)2 - 3
C. X= -3(y + 3)2 + 5
D. y = -3(x - 5)2-3
The vertex of a parabola is written as (h,k) so h = 5 and k = -3.
H is subtracted from x inside parentheses and k is added at the end of the equation.
The equation is also written as y =
The answer should be D.
Answer c also works, so there are two correct answers.
IM TAKING AN EXAM AND I NEED SO MUCH HELP!!
Show how to find the inverse of f(x) = x^3 - 5. Calculate 3 points on f(x) and use these points to show that the inverse is correct.
Answer:
[tex]f^{-1}(x) = \sqrt[3]{x+5}[/tex]
Step-by-step explanation:
A function [tex]f^{-1}[/tex] is the inverse of f if whenever y =f(x) and [tex]x =f^{-1}[/tex]
To find the inverse of f(x) = [tex]x^{3}[/tex] - 5, we use the following steps:
Step 1 : Put y for f(x) and solve for xy = [tex]x^{3}[/tex] - 5
<=> [tex]x^{3}[/tex] = y + 5
<=> x = [tex]\sqrt[3]{y+ 5}[/tex]
Step 2: Put [tex]f^{-1}(y)[/tex] for x, we have:[tex]f^{-1}(y) =\sqrt[3]{y+5}[/tex]
Step 3: Interchange y =x, we have[tex]f^{-1}(x) = \sqrt[3]{x+5}[/tex]
Let Calculate 3 points on f(x)
x = 0 => y = -5
x = 1 => y = -4
x = 2 => y = 3
Let Calculate 3 points on [tex]f^{-1}[/tex] (x)
x = -5 => y = 0
x = -4 => y = 1
x = 3 => y = 2
Yes, the inverse is correct because:
the domain of the inverse function is the range of the original function the range of the inverse function is the domain of the original functionSimplify 4^5/4^3 and show steps
Answer:
16
Step-by-step explanation:
4^5/4^3
4^5-3
4^2
16
Hope this helps :)
Danielle had planned her gift basket to be priced at $50 with a 40% gross margin. She forgot packaging costs which will be $3 per unit. If she still keeps the price at $50, how much will her gross margin percentage be after packaging costs?
a) 30%
b) 34%
c) 43%
d) 47%
The gross margin percentage after packaging costs would be a) 30%.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Danielle had planned her gift basket to be priced at $50 with a 40% gross margin.
let, The original price be 'x'.
Therefore, $50 is 140% of 'x' which is,
(140/100)×x = 50.
1.4x = 50.
x = 50/1.4.
x = 35.71.
Now, The packaging cost is $3 which makes the cost of the product 38.71.
So, (50/38.71)×100.
= 29% gross margin.
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the lines on a coordinate plane are perpendicular.
perpendicular lines form what type of angles?
Final answer:
Perpendicular lines on a coordinate plane intersect to form right angles, which are precisely 90°. The slopes of perpendicular lines are negative reciprocals of each other.
Explanation:
When two lines on a coordinate plane are described as being perpendicular, this means they intersect to form right angles, which are angles of 90°. It's important to recognize that perpendicular lines have slopes that are negative reciprocals of each other. For example, if one line has a slope of 2, a line perpendicular to it would have a slope of -1/2. These slopes ensure that the angles formed between the lines are exactly 90 degrees.
In geometry and physics, this concept is further explored with orthogonal vectors, which are two vectors with directions that differ by exactly 90°, synonymous with perpendicular vectors. Their importance lies in various applications, such as breaking down a force into components acting along perpendicular axes.
Help please...........................
Answer: n=3, hope this helps! c:
-5x+2=22
A. 96
B. 6
C. 4
D. -4
O need the answer
Where would 4 cups be placed on the number line
Answer:
D
Step-by-step explanation:
There are 2 cups in a pint, so 3 cups would be 1.5 pints. :)
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Divide.
1/8 ÷ 9
Enter your answer as a fraction in simplest form by filling in the boxes.
Answer:
1/72
Step-by-step explanation:
Answer:
1/72
Step-by-step explanation:
1/8 divided by 9 = 1/8 times 1/9.
We have ti flip 9/1 so we get 1/9
You multiply 9 by 8 you get 72
so the answer is 1/72
A photo is printed on a 20-inch by 24-inch piece of paper. The photo covers 320 square inches and has a ubiform border. What is the width of
the border?
Answer:2 in.
Step-by-step explanation:
Given
Dimension of photo frame is [tex]20\ in.\times 24\ in.[/tex]
If the photo cover an area of [tex]320\ in.^2[/tex]
Suppose x be the width of border
Therefore dimension of frame without border is
[tex]A'=(20-2x)(24-2x)[/tex]
And [tex]A'[/tex] must be equal to [tex]320\ in.^2[/tex]
So,
[tex]\Rightarrow (20-2x)(24-2x)=320[/tex]
[tex]\Rightarrow (10-x)(12-x)=80[/tex]
[tex]\Rightarrow 120-10x-12x+x^2=80[/tex]
[tex]\Rightarrow x^2-22x+40=0[/tex]
[tex]\Rightarrow x^2-20x-2x+40=0[/tex]
[tex]\Rightarrow (x-2)(x-20)=0[/tex]
Thus there are two values of x out of which [tex]x=20\ in.[/tex] is not valid because it is not feasible
thus width of border is [tex]x=2\ in.[/tex]
1. Using the floorplan below, calculate the total area of the space.
YOU MUST SHOW ALL WORK FOR CREDIT.
Breakfast)
nook
Kitchen
Formal Dining
1 unit = 5 feet
Answer:
i believe it is 185 feet
The Cole family owns an above-ground circular swimming pool that has walls made of aluminum.
Find the length (l) of aluminum surrounding the pool as shown if the radius is 15 feet.
(use π=3.14 )
Type your result in an empty box provided below rounded to the nearest tenth.
Answer:
Step-by-step explanation:
Heaat
Answer:
I = 94.2 ft
Step-by-step explanation:
The formula for circumference is
[tex]2\pi r[/tex]
if the radius is 15 all you need to do is plug it in and solve
[tex]2\pi 15[/tex]
multiply 2 and 15
30
multiply 30 and pi
94.2
add units and you're done
(if you use the symbol for pi in the calculator it gives you 94.25 but it said to use 3.14 for pi. If you use the symbol pi it's way more than just 3.14)
Plz plz plz plzplzplzplz help me plz plz help plz plz show me plz plz thx plz
Answer: 97
Step-by-step explanation:
4,074 / 42
hope this helped
The head-to-tail length of a species of fish is normally distributed, with a
mean of 17.4 cm and a standard deviation of 3.2 cm. One fish is 16.3 cm
long. What is the score of the length of this fish? Round your answer to two
decimal places.
A. 0.54
B. 0.34
C. -0.34
D. -0.54
Answer:
C. -0.34
Step-by-step explanation:
We have that for a normal distribution, the value of z can be calculated using the following formula:
z = (x - m) / sd
where x is the value to evaluate, m the mean and sd the standard deviation, we have those values x = 16.3, m = 17.4 and sd = 3.2
if we replace we have:
z = (16.3 - 17.4) /3.2
z = -0.3437
if we round to 2 decimal places, it would be -0.34, that is, the answer is C.
The z-score for a fish measuring 16.3 cm, with a mean length of 17.4 cm and a standard deviation of 3.2 cm, is -0.34.
The score of the length of the fish, also known as the z-score, is calculated by subtracting the mean from the observed value and then dividing by the standard deviation. Using the provided data, we have a mean (μ) of 17.4 cm and a standard deviation (σ) of 3.2 cm. The fish in question measures 16.3 cm.
To find the z-score, the calculation is as follows:
Z = (X - μ) / σ
Z = (16.3 cm - 17.4 cm) / 3.2 cm
Z = -1.1 cm / 3.2 cm
Z = -0.34 (rounded to two decimal places)
Therefore, the z-score for a fish that is 16.3 cm long is -0.34, which corresponds with answer option C.
a scale drawing if a living room is shown below. the scale used to create the drawing is 1in. = 2ft ANSWER NEEDED QUICK PIC ABOVE
Answer:
144 ft^2
Step-by-step explanation:
6 inches to feet (comparison based on scale) would make each side 12 feet long (6x2). 12 times 12 is 144.
Answer:
144
Step-by-step explanation:
A catapult launches a boulder with an upward velocity of 120 ft/s. The height of the boulder, h,
in feet after t seconds is given by the function h=-167 + 120t + 10. How long does it take to
reach maximum height? What is the boulder's maximum height? Round to the nearest
hundredth, if necessary.
a. Reaches a maximum height of 235.00 feet in 3.75 seconds.
b. Reaches a maximum height of 10.00 feet in 7.50 seconds.
c. Reaches a maximum height of 7.58 feet in 3.75 seconds.
d. Reaches a maximum height of 15.16 feet in 7.5 seconds.
Answer:
Reaches a maximum height of 235.00 feet in 3.75 seconds.
Step-by-step explanation:
The height of the boulder, h, in feet after t seconds is given by the function is given by :
[tex]h=-16t^2+120t+10[/tex] .....(1)
For maximum height, put [tex]\dfrac{dh}{dt}=0[/tex]
i.e.
[tex]\dfrac{d(-16t^2+120t+10)}{dt}=0\\\\-32t+120=0\\\\32t=120\\\\t=3.75\ s[/tex]
Put t = 3.75 in equation (1). So,
[tex]h=-16(3.75)^2+120(3.75)+10\\\\h=235\ \text{feet}[/tex]
So, the boulder's maximum height is 235 feets and it takes 3.75 s to reach to its maximum height.
Janice has car insurance that she must pay four times a year. If each payment is $156, how much money should she set aside each month to
cover her car insurance?
OA $13
OB. $26
oc $39
OD. $52
Answer:
C
i hope this helped you
Answer:
D
Step-by-step explanation:
cause if you pay 4 times a year that means you set money aside every three months which means that you set 52 dollars every month
Select all the correct locations on the table.
Classify each situation as exponential growth, exponential decay, or linear
Answer:
Situation 1 is exponential decay. Situation 2 is linear. Situation 3 is exponential growth.
Step-by-step explanation:
Situation 1 is exponential decay because it declined in a non linear way.
600-480=120 480-364=116
Situation 2 is linear because when it declined it has a dependent to another.
400-340=60 340-280=60
Situation 3 is exponential growth because is increases.
Which graph represents this sysytem? y=3 x+y=4
Answer:
On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0).
Step-by-step explanation:
Isabell some music playlist has 12 rock songs 15 pop songs 13 hip-hop songs and 10 oldies songs.if she sets the playlist on random shuffle what is the probability that the first song will be a pop song?
Answer:
3/10 or 30%
Step-by-step explanation:
it is the number of pop songs in the list divided by all of the songs combined.
so 15 pop songs
over
12+13+10+15=50
15/50 is you answer
simplify and get
3/10
two similar trapezoids have areas of 180 cm2 and 45cm2. what is their ratio of similarity
The ratio of similarity between the two trapezoids is 2:1, which means that the linear dimensions of the larger trapezoid are twice those of the smaller one.
To find the ratio of similarity between two similar trapezoids with areas of 180 [tex]cm^2[/tex] and 45 [tex]cm^2[/tex], we use the principle that the ratio of the areas of similar figures is equal to the square of the ratio of their corresponding linear dimensions. In other words, if the ratio of similarity (scale factor) between the linear dimensions of two similar figures is 'k', then the ratio of their areas is '[tex]k^2[/tex]'.
Let the ratio of similarity be 'k'. Then we have 180/45 = k^2. Simplifying this, we get 4 = [tex]k^2[/tex] and thus, k = 2. This means the linear dimensions of the larger trapezoid are twice those of the smaller one.
Therefore, the ratio of similarity between the two trapezoids is 2:1.
Find m<_6 if m<_8 = 119 degrees.
Angle 6 and angle 8 are corresponding angles, because they are in the same position, but on different parallel lines. Corresponding angles are congruent. So, if the measure of angle 8 is 119 degrees, then the measure of angle 6 is 119 degrees.
Hope this helps! :)
the radius of a circle is 5 inches what is the area of a sector biunded by 180 degrees arc
The area of a sector with a radius of 5 inches and a 180-degree arc is half the area of the full circle, resulting in 39.27 square inches when rounded.
Explanation:The area of a sector of a circle with radius 5 inches that is bounded by a 180-degree arc can be found by first calculating the area of the entire circle and then taking half of that area, since 180 degrees is half of the full 360 degrees of a circle. The formula to calculate the area of a circle is A = πr². For a radius (r) of 5 inches, the entire circle's area would be A = π(5 inches)².
Thus, the entire circle area is A = 3.1415927 × (5 inches)² = 78.53981633974483 square inches. Since the sector is half of the circle, the area of the sector would be 39.269908169872415 square inches, or when rounded to two decimal places, 39.27 square inches.
evaluate the expression for q=8.
7q
q=8
soo
7(8)=64
64 is the final answer.