To simplify the expression 5.2 + 3.6x - 8 + x, combine like terms to get -2.8 + 4.6x, which is the final simplified expression.
Explanation:The student's question involves simplifying the expression 5.2 + 3.6x – 8 + x. To simplify the given algebraic expression, combine like terms. Like terms in this expression are the constant terms (5.2 and -8) and the variable terms (3.6x and x).
First, add the constant terms together:
5.2 - 8 = -2.8
Then, combine the variable terms:
3.6x + x = (3.6 + 1)x = 4.6x
Now, put the constants and variable terms together to get the simplified expression:
-2.8 + 4.6x
To check if the simplified expression is reasonable, ensure that all like terms have been correctly combined. There is no further simplification possible, so this is the final answer.
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A normal distribution has a mean of 186.4 and a standard deviation of 48.9.
What range of values represents the upper 2.5% of the data?
a
X > 235.3
b
X > 333.1
c
X > 284.2
d
X > 186.4
We have been given that a normal distribution has a mean of 186.4 and a standard deviation of 48.9. We are asked to find the range of value that represents the upper 2.5% of the data.
We know that upper 2.5% of data would be 97.5% of data.
We will use z-score formula to solve our given problem.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
z = z-score,
x = Random sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
Now we will use normal distribution table to find z-score corresponding to 97.5% area or 0.975.
We can see from the normal distribution table that z-score corresponding to area 0.975 is [tex]1.96[/tex].
[tex]1.96=\frac{x-186.4}{48.9}[/tex]
Let us solve for x.
[tex]1.96\cdot 48.9=\frac{x-186.4}{48.9}\cdot 48.9[/tex]
[tex]95.844=x-186.4[/tex]
[tex]95.844+186.4=x-186.4+186.4[/tex]
[tex]282.244=x[/tex]
Therefore, the range [tex]x>282.244[/tex] represents the upper 2.5% of the data.
The perimeter of a rectangle is 128 cm. The length of the rectangle is three times longer than the width. What is the length and width of the rectangle?
Answer:
l=16 cm
w=48 cm
Step-by-step explanation:
perimeter of rectangle formula:
2l+2w
where
3w=l
and w=w
so
2(3w)+2w=128
6w+2w=128
8w=128
w=16
now substitute 16:
2l+2(16)=128
2l+32=128
2l=96
l=48
The length is 48 cm and width is 16 cm.
what is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values. . In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
given:
perimeter of a rectangle is 128 cm.
let the width be x
length= 3x
So, perimeter of a rectangle is 128 cm.
2( l + w)= 128
x+ 3x= 64
4x= 64
x= 16
Hence, the length is 48 cm and width is 16 cm.
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PLEASE HELP ME
. Find the surface area of the triangular pyramid. *
Answer:
89.4 yd
Step-by-step explanation:
Surface area of a triangular pyramid = B × H ÷ 2
6 × 5.2 ÷ 2 = 15.6
6 × 8.2 ÷ 2 = 24.6
6 × 8.2 ÷ 2 = 24.6
6 × 8.2 ÷ 2 = 24.6
15.6 + 24.6 + 24.6 + 24.6 = 89.4
Mr. Smith opened an account with a deposit of $750. The bank pays 6% interest compounded annually on this account. Mr. Smith makes no additional deposits or withdrawals. How much interest will the account have earned at the end of 4 years? *
The final balance is $897.51
Step-by-step explanation:
Which property can you use to show that 3x +{2x+4} is equivalent to {3x + 2x} + 4
Answer:
3x+2x=5x but 4 can't add to 3x and 2x
Answer:
6x – 3x + 9y + 4 + 11 is equivalent to 3(x + 3y + 5)
Step-by-step explanation:
Find the missing factor. 5y^2+4y-1=(5y-1)()
Answer:
(5y−1)(y+1)
Step-by-step explanation:
Answer:
(y + 1 )
Step-by-step explanation:
Given
5y² + 4y - 1
Consider the factors of the product of the y² term and the y- term which sum to give the coefficient of the y- term
product = 5 × - 1 = - 5 and sum = + 4
The factors are + 5 and - 1
Use these factors to split the y- term
5y² + 5y - y - 1 ( factor the first/second and third/fourth terms )
= 5y(y + 1) - 1(y + 1) ← factor out (y + 1) from each term
= (y + 1)(5y - 1)
The missing factor is (y + 1)
Kanesha wants to find out if people in her community would support a dog park. Which populations would be appropriate to sample for the survey?
A. People shopping at local pet store.
B. Parents of small children in the community.
C. Children attending the local school.
D. Owners of local businesses.
Answer:
a
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
What are the measures of those two angles? I’ll mark brainliest!
Answer:
Two angles of a quadrilateral : 220 and 90 deg.
The other two angles (x and y) are in ratio 2:3.
We have:
x + y = 360 - 220 - 90 = 50 (property of sum of 4 angles in quadrilateral)
x/y = 2/3 => x = 2y/3
=>2y/3 + y = 50
=> 5y/3 =50
=> 5y = 150
=> y = 30
=> x = 2 x 30/3 = 20
=> Two other angles are 20 and 30 deg
Hope this helps!
:)
Jason owns a food truck that sells tacos and burritos. He sells each taco for $4.75 and each burrito for $7.50. Yesterday Jason made a total of $790 in revenue from all burrito and taco sales and there were twice as many burritos sold as there were tacos sold. Write a system of equations that could be used to determine the number of tacos sold and the number of burritos sold. Define the variables that you use to write the system.
let t be the number of tacos sold
let b be the number of burritos sold
Step-by-step explanation:
b=2t
4.75t+7.50b=790
To solve the problem, set up two variables T and B for the number of tacos and burritos sold. Two equations are formed: B = 2T (since twice as many burritos as tacos were sold) and 4.75T + 7.50B = 790 (from the total revenue). Solve these to find T and B.
Explanation:To determine the number of tacos and burritos sold by Jason's food truck, we need to establish two variables: let T represent the number of tacos sold, and let B represent the number of burritos sold. Given that burritos are sold at a ratio of two to every one taco, we can express this relationship with the equation B = 2T. Next, using the given prices of tacos ($4.75) and burritos ($7.50), along with the total revenue of $790, we can write the budget constraint equation as 4.75T + 7.50B = 790. These two equations together form the system of equations that can be solved to find the number of tacos (T) and burritos (B) sold.
He has between 10 and 20 batteries. He counts the batteries by putting them into piles of 4 and finds that he has 3 left over. He then counted them by putting them into piles of 3 and found that he had one left over. How many batteries does he have?
Answer:
15 batteries
Step-by-step explanation:
If he puts the batteries in piles of 4, and there is 3 left over, the number of batteries he can have is:
2 piles: 4*2 + 3 = 11
3 piles: 4*3 + 3 = 15
4 piles: 4*4 + 3 = 19
Then, when he puts in piles of 3, there is no batteries left over, so the number of batteries is a multiple of 3.
From the 3 possibilities above (11, 15 and 19), only the number 15 is a multiple of 3, so the number of batteries is 15.
The graph of the function f(x) = x2 + 8x + 12 is shown. Which statements describe the graph? Check all that apply.
The vertex is the maximum value.
The axis of symmetry is x = –4.
The domain is all real numbers.
The range is all real numbers.
The function is increasing over (–∞, –4).
The x-intercepts are at (–6, 0) and (–2, 0).
Answer:
B C F
explanation:
Took the test
Answer:
B C F
Step-by-step explanation:
edge
Apply the distributive property to factor out the greatest common factor.
32+44=
Answer:
4(8 + 11).
Step-by-step explanation:
32 - 44
The greatest common factor is 4 so we have
4(8 + 11).
Rectangle QUAD has coordinates Q(4,5), U(4,10), A(11,10), and D(11,5). Upper Q prime Upper U prime Upper A prime Upper D primeQ′U′A′D′ is the image of QUAD after a dilation with center (0,0) and scale factor 5. What is the length of segment Upper Q prime Upper U primeQ′U′?
Answer:
25
Step-by-step explanation:
Answer: 25
find the length of segment QU.
First, we must find out what the coordinates are.
Q=(4,5) U=(4,10)
Then, Setup your equation by making the first coordinate pair equal. So,
Q= (4,5) would now equal Q=(5,5). That means we added 1. (when you add x ((x=the number you add to make equal)) you add x to the other side as well)
So, now we would add 1 (or how many you got) to U. Thus,
U=(4,10) would now equal Q=(5,10).
Next, set up the equation.
[tex]\sqrt{(Q)^{2} +(U)^{2}[/tex] (Q=(5,5) and U=(5,10).)
* You will now be subtracting the coordinates so, Q=(5-5) and U=(5-10)*
Next, Substitute the equation.
[tex]\sqrt{(5-5^{2} +(5-10)^{2}[/tex]
After, we solve.
[tex]\sqrt{0^{2} +(5-10)^{2}[/tex]
*the sum of two opposites equals 0. 5-5=0*
Next, Subtract (5-10).
[tex]\sqrt{0^{2} +(-5)^{2}[/tex]
Next, 0 raised to any positive power equals 0
[tex]\sqrt{0+(-5)^{2}[/tex]
Next, When adding or subtracting 0, the quantity does not change.
[tex]\sqrt{(-5)^{2}[/tex]
Next, Reduce the index of the radical and exponent 2.
[tex]|-5| = 5[/tex]
So, The length of segment is 5.
Now, find the length of segment Upper Q'U', multiply the length of segment QU by the scale factor.
scale factor in this equation is 5.
Now, multiply.
5·5 = 25
So, the length of segment Q'U' is 25.
The length of segment Q'U' after the dilation with a scale factor of 5 is 25 units.
To find the length of segment Q'U' after the dilation with a scale factor of 5, we can calculate it step by step:
1. Calculate the new coordinates of Q' and U' after the dilation with a scale factor of 5 and center (0,0):
Q' coordinates: (4 5, 5 5) = (20, 25)
U' coordinates: (4 5, 10 5) = (20, 50)
2. Determine the distance between Q' and U' using the distance formula:
- Horizontal distance: 20 - 20 = 0
- Vertical distance: 50 - 25 = 25
3. Calculate the length of segment
using the Pythagorean theorem:
- Length = sqrt(0^2 + 25^2)
- Length = sqrt(0 + 625)
- Length = sqrt(625)
- Length = 25 units
Therefore, the length of segment Q'U' after the dilation with a scale factor of 5 is 25 units.
Alfonso graphs the inequality x greater-than negative 8 using the steps below.
Step 1: Draw a number line, and place an open circle at –8.
A number line going from negative 13 to negative 3. An open circle is at negative 8.
Step 2: Shade to the left of –8 to represent the infinite solutions to x greater-than negative 8.
A number line going from negative 13 to negative 3. An open circle is at negative 8. Everything to the left of the circle is shaded.
Step 3: Check work by substitution.
x = negative 9
Negative 9 greater-than negative 8 False
Which best describes the situation?
i know its kinda hard
A-The graph is incorrect. He should have used a closed circle at –8.
B-The graph is incorrect. He should have shaded to the right of –8.
C-The graph is correct. He should have checked his work with a number that was not on the shaded portion of the graph.
D-The graph is correct. He should have checked his work using –8.
Answer:
B-The graph is incorrect. He should have shaded to the right of –8.
Step-by-step explanation:
We examine the steps Alfonso follows in graphing the inequality x > -8.
Step 1: Draw a number line, and place an open circle at –8.
A number line going from negative 13 to negative 3. An open circle is at negative 8.
The first step is correct, since we use an open circle for > or < and a closed circle for [tex]\leq \:or\: \geq[/tex].
Step 2: Shade to the left of –8 to represent the infinite solutions to x greater-than negative 8.
This step is incorrect since values to the left are always less than.
He should have shaded to the right of -8.
The error made is Option B.
CHECK:
x=-7
-7>-8 (TRUE)
Answer:
I got the answer B too.
Step-by-step explanation:
All you have to do is re read your question
HOPE THIS HELPS:)
STAY SAFE
What is the expanded form of the series represented below?
S5 = [-3+(k=16]
-3+2+7+12+17
-3+3+8+13+ 18
O2+7+12+17+22
5+2+(-1)+(-4)+(-7)
Pls hurry for a test
Answer:a
Step-by-step explanation:
Simplify 6 x 10−7 2 x 105 .
Answer:
-49
Step-by-step explanation:
it would be this because first we would have to figure out what 6*10 is that why we know what to distribute . so once we figure it out , which is 70 . We would then subtract 14 from 70 . Since 7 is right next to 2 we would then multiply it to get to 14. Once we get that you should get 56, from there you would subtract 56 to 105 , and get your answer.
a town has a population of 14000 and grows at 4.5% each year. to the nearest tenth of a year how long will it be until the population will reach 41500
Answer:
about 6.6 years
Step-by-step explanation:
41,500=14,000*.45*x
41,500=6,300*x
41,000/6,300=x
6.5873=x
6.6=x
Answer:
24.7
Step-by-step explanation:
A house purchased for $226,000 has lost 4% of its value each year for the past five years. What is it worth now?
Answer:
The answer would be $184,274.23.
Step-by-step explanation:
After a 4% annual decrease in value over five years, a house that was bought for $226,000 would be worth around $183,896.7.
Explanation:The student's question pertains to a situation where a house's value depreciates, in this case, at a rate of 4% per year for five years. To find out how much the house would be worth now, we need to employ the formula for depreciations, that is P = P0 (1 - r)^n, where P is the final value, P0 the initial value, r the rate of decrease and n the number of periods the decrease has occurred over.
In this case, P0 would be the initial value of the house $226,000, r would be 4% (or 0.04 as a decimal), and n would be the number of years, which is 5. Substituting these values into the formula gives us and calculated we get P = $226,000 * (1 - 0.04)^5 = $183,896.7.
So after a 4% annual decrease in value over five years, the house that was bought for $226,000 would now be worth around $183,896.7.
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P(1, 0) corresponds to
( , ) on the sine graph.
Answer:
Step-by-step explanation:
P(1,0) corresponds to (0,0)
P(0,1) corresponds to (90,1)
P(-1,0) corresponds to (180,0)
P(0,-1) corresponds to (270,-1)
The points (0, 0), (0, 1), (-1, 0), (0, -1) when traced on the graph respectively correspond to; (0, 0), (90, 1), (180, 0), (270, -1)
How to Interprete Sine Graphs?A) From the given graph, we can see that the point P(1,0) when traced corresponds to (0,0) because sin 0 = 0.
B) From the given graph, we can see that the point P(0,1) when traced corresponds to (90, 1) because sin 90 = 1.
C) From the given graph, we can see that the point P(-1,0) when traced corresponds to (180, 0) because sin 180 = 0.
D) From the given graph, we can see that the point P(0,-1) when traced corresponds to (270,-1) beacuse sin 270 = -1
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Which is the graph of f(x) = -(x + 3)(x + 1)?
Answer:
Step-by-step explanation:
Setting f(x) = -(x + 3)(x + 1) = 0 leads to identifying two roots/solutions of this equation: x = -3 and x = -1. The axis of symmetry is a vertical line halfway between these two roots: x = -2. This x = -2 is also the x-coordinate of the vertex. Evaluating f(x) = -(x + 3)(x + 1) at x = -2 gives us the y-coordinate of the vertex: y = -(-2 + 3)(-2 + 1) = -(1)(-1) = 1.
In summary, the vertex is at (-2, 1) and the two x-intercepts are (-3, 0) and (-1, 0). The y-intercept is found by setting x = 0 and finding y:
f(0) = -(0 + 3)(0 + 1) = -3, or (0, -3)
Next time, please share the answer choices. Thank you.
Answer:
B
Step-by-step explanation:
Edge 2021
ANSWER ALL FIRST CORRECT ANSWER GETS BRAINLIEST, THANKS AND FIVE STAR!!
Answer:
1. -5
2. -10
3. 12
4. -6
5. 20
6. -7
7. -10
8. -19
9. 4
10. -5
11. -10
12. 8
13. 2
14. -8
15. -1
16. 9
17. -7
18. 2
19. 4
20. -17
21. 0
22. -10
23. 2
24. 1
25. 9
26. -6
27. -12
28. 4
29. -3
30. -68
Answer:
it was nt quite old enough to be a buck
Step-by-step explanation:
Radians and arc length
Answer:
arc length "s" = radius * central angle in radians
radius = arc length "s" / central angle
radius = "s" / 1.2
arc length "s" = r * 1.2
Step-by-step explanation:
22.2, -0.2, 2.02 smallest to largest
Answer:
-0.2, 2.02, 22.2
Explanation:
-0.2 is below zero, 2.02 is 20.18 less than 2.02
Rearrange your equation from part A by setting it equal to 0 and substituting y for 0. Then write the equation in the form y = (x – h)2 – c.
Answer:
y = (x - 1)^2 - 8
Step-by-step explanation:
Your answer from part A should be: (x - 1)^2 = 8
You are simply changing the format of the equation from
0 = (x - 1)^2 - 8 to y = (x - 1)^2 - 8
Hope this helps!
Answer:
y = (x-1)² - 8
Step-by-step explanation:
The response from part A is (x – 1)2 = 8, where h = 1 and c = 8.
Set the equation equal to 0:
0 = (x – 1)2 – 8.
Substitute y for 0 and keep the equation rewritten in the form y = (x – h)2 – c:
y = (x – 1)2 – 8.
A number line is numbered in tenths Describe where you would plot √87.35
Answer:
Plot at 9.3
Step-by-step explanation:
Take the square root of 87.35
sqrt(87.35)
9.346122191
Rounding to the nearest tenth
9.3
Plot at 9.3
The mass of the cylinder is 50,000 g. Find the density of the cylinder to the nearest tenth
answer choices
0.7 g/mm3
81.2 g/mm3
2.7 g/mm3
0.4 g/mm3
Answer:
Density of the Cylinder = 2.7 g/mm³
Step-by-step explanation:
Density of a cylinder is calculated using the formula =
Mass of the Cylinder ÷ Volume of the Cylinder
Step 1
The First step is to find the Volume of the Cylinder.
Volume of a Cylinder = πr²h
In the attached image , we are given:
Diameter of the Cylinder = 28mm
Radius of the Cylinder = Diameter ÷ 2 = 28mm ÷ 2
Radius of the Cylinder (r) = 14mm
Height of the Cylinder (h) = 30mm
The Volume of the Cylinder = πr²h
= π × (14mm)² × 30mm
= 18472.564803 mm³
Step 2
The second step would be to find the Density of the Cylinder.
Density of the Cylinder = Mass of the Cylinder ÷ Volume of the Cylinder
Mass of the Cylinder = 50,000g
Volume of the Cylinder = 18472.564803 mm³
Density of the Cylinder = 50,000g ÷ 18472.564803 mm³
= 2.7067167193 g /mm³
Approximately the Density of the Cylinder = 2.7 g/mm³
What is the range of possible sizes for side xxx? < x <
According to the theory of the Triangle Inequality, so, the total of the 2 sides of the triangle must be larger than the length of the third side. Therefore, the possible length of a triangle is given by the difference of two sides x the sum of two sides.
Therefore,
[tex]\to 4.3-2.1< x <4.3+2.1 \\\\\to 2.2< x <6.4 \\\\[/tex]
So, the final answer is "[tex]2.2<x<6.4[/tex]" which is the possible length of x.
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The range of possible sizes for side 'x' is from 1.5 to 4.5, inclusive of both endpoints.
Explanation:The question "What is the range of possible sizes for side xxx?" refers to finding the possible values that the variable 'x' can take. From the information provided, we understand that 'x' can be any number in the inclusive range from 1.5 to 4.5, which can be denoted mathematically as 1.5 ≤ x ≤ 4.5. This means that the smallest value 'x' can be is 1.5, and the largest value is 4.5. The range of possible sizes for 'x' is therefore between 1.5 and 4.5, including both of these endpoints.
* Required
How do you name a prism or pyramid? *
10 points
O
by
by the shape of its face
O
by the number of edges it has
O
by the number of vertices it has
O
by the shape of its base
What parts of prism make up its faces? Check all that apply. *
10 points
bases
Answer:
by the number of edges it has
Step-by-step explanation:
cuz a prism has more sides than a pyramid
Find the circumference and area of a circle whose radius is 12.4 cm.Give your answer to the nearest centimeter (whole #). Circumference = cm Area = cm2
Final answer:
The circumference of the circle is approximately 78 cm and the area of the circle is approximately 484 cm².
Explanation:
The circumference of a circle can be found by using the formula:
Circumference = 2πr, where r is the radius of the circle.
Given that the radius is 12.4 cm, we can substitute this value into the formula:
Circumference = 2π(12.4 cm)
Using an approximation of π as 3.14, the calculation becomes:
Circumference = 2(3.14)(12.4 cm) = 77.9 cm
Therefore, the circumference of the circle is approximately 78 cm (to the nearest whole number).
The area of a circle can be found by using the formula:
Area = πr²
Substituting the given radius into the formula:
Area = 3.14(12.4 cm)² = 483.864 cm²
Therefore, the area of the circle is approximately 484 cm² (to the nearest whole number).
A 10 foot ladder is placed 4-feet from the edge of a building. How far up the building does the ladder reach? Round your answer to the nearest tenth of a foot.
A:10.8 feet
B:9.2 feet
C:2.4 feet
D:3.7 feet
The ladder is 9.2 feet up the building
The length (L) of the ladder is given as:
[tex]L = 10ft[/tex]
The distance (d) from the edge of the building is
[tex]d = 4ft[/tex]
The distance up the ladder is the height (h) of the ladder on the wall.
This is calculated using the following Pythagoras theorem
[tex]L^2 = d^2 + h^2[/tex]
So, we have:
[tex]10^2 = 4^2 + h^2[/tex]
Evaluate the exponents
[tex]100 = 16 + h^2[/tex]
Subtract 16 from both sides
[tex]84 = h^2[/tex]
Take square roots of both sides
[tex]9.2 = h[/tex]
Rewrite as
[tex]h =9.2[/tex]
Hence, the ladder is 9.2 feet up the building
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