What compound inequality represents the phrase? Graph the solutions.
all real numbers that are greater than –8 and less than 8
Find the value of the variable that makes the statement true:
cube root of 3375= m.
what is m please asap.
Answer:
m=15
Step-by-step explanation:
cube root of 3375 =m
We need to solve the equation for m
[tex]\sqrt[3]{3375} = m[/tex]
In order to solve for m we need to find the cube root of 3375
3375 can be written as 3 times 3 times 3 times 5 times 5 times 5
[tex]\sqrt[3]{3375} = m[/tex]
[tex]\sqrt[3]{3 \cdot 3 \cdot 3 \cdot 5 \cdot 5 \cdot 5} = m[/tex]
For same three factors inside the cube root we pull out one factor outside the cube root
[tex]\sqrt[3]{3 \cdot 3 \cdot 3} = 3[/tex]
[tex]\sqrt[3]{3 \cdot 3 \cdot 3 \cdot 5 \cdot 5 \cdot 5} = m[/tex]
[tex]3 \cdot 5 = m[/tex]
m= 15
The value of the variable that makes the statement true is
m = 15
Cube Root FunctionsThe given equation is:
[tex]\sqrt[3]{3375} = m[/tex]
We are looking for a number that we can multiply by itself 3 times to get 3375
Note that the given equation can be re-written as:
[tex]m =3375^{\frac{1}{3}[/tex]
This can be further simplified as:
[tex]m=15^{3(\frac{1}{3} )}\\\\m=15[/tex]
Therefore, the value of the variable that makes the statement true is m = 15
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A university found that 10% of its students withdraw without completing the introductory statistics course. assume that 20 students registered for the course.
what is the meaning os slpoe in math and please give an example for
y=2x-1;(-2,2)
Slope in math is the difference in y-values divided by x-values.
The slope helps determine the steepness of a line. Y-intercept is the y-value when x=0. The formula for slope, denoted as m, is (y2-y1)/(x2-x1).
Example: For the equation y = 2x - 1, if we have the point (-2, 2), we can calculate the slope by substituting the values into the formula: m = (2-(-1))/(-2-0) = 3/-2 = -1.5.
Y-intercept is the y-value when x=0, or where the graph crosses the y-axis.
HELP PLZ!!!! A courtyard in the shape of a right triangle is set in the middle of three square office buildings, with one office building along each side. Which statement is true about the three office buildings?
solve for w.
-3w+2=-10w+30
-3w+2=-10w+30
add 3 w to each side
2=-7w+30
subtract 30 from each side
-28 = -7w
divide both sides by -7
w = 4
double check
-3(4) +2 = -10
-10(4) +30 = -10
so w = 4
Gambler is deciding whether or not to take a bet. she must pay $40 to take the bet, but if she wins, she willprofit$225.theprobability that she wins the bet is ¼. what is the player’s expected value in this situation
The length of the longer leg of a right triangle is 6cm more than twice the length of the shorter leg. The length of the hypotenuse is 9cm more than twice the length of the shorter leg. Find the side lengths of the triangle.
Length of the shorter leg:
cm
Length of the longer leg:
cm
Length of the hypotenuse:
cm
By defining the shorter leg of the triangle as 'x' and applying the Pythagorean Theorem to solve the given equations, we find that the shorter leg is 3cm, the longer leg is 12cm, and the hypotenuse is 15cm.
Explanation:Let's define the shorter leg of the triangle as 'x'. As given, the longer leg would be '2x + 6' and the hypotenuse would be '2x + 9'.
To solve for the lengths of the sides, let's use the Pythagorean Theorem, which says that the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, the equation would be (2x + 6)^2 + x^2 = (2x + 9)^2.
Solve this equation by expanding, collecting similar terms, and factoring. You'll end up with x = 3. Therefore, the shorter leg of the triangle is 3cm, the longer leg is 2x + 6 = 2*3 + 6 = 12cm, and the hypotenuse is 2x + 9 = 2*3 + 9 = 15cm.
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Subtract 8-4 1/2. A. 3 B. 4 C. 4 1/2 D. 3 1/2
Subtraction of 8-4 1/2 is 3 1/2.
The correct option is D.
To subtract 8 - 4 1/2, we need to convert the mixed number 4 1/2 into an improper fraction.
To do this, we multiply the whole number (4) by the denominator (2), which gives us 8. Then we add the numerator (1) to get 9. So, 4 1/2 is equivalent to the improper fraction 9/2.
Now, we can subtract 8 from 9/2. To subtract fractions, the denominators must be the same. We can rewrite 8 as 8/1 to have a common denominator with 9/2.
Subtracting 8/1 from 9/2 gives us (8 - 9/2).
To subtract fractions, we need a common denominator, which is 2 in this case.
Converting 8/1 to have a denominator of 2, we get 16/2.
Now we can subtract the fractions: (16- 9)/2 = 7/2.
Therefore, the answer is 7/2, which can also be expressed as 3 1/2.
So the correct answer is D. 3 1/2.
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The value of y is inversely proportional to the value of x. When y=24, x=4. What is the value of y when x=6?
The value of [tex]\( y \)[/tex] when x = 6 is 16.
Given that [tex]\( y \)[/tex] is inversely proportional to [tex]\( x \)[/tex], we can write the relationship as:
[tex]\[ y = \frac{k}{x} \][/tex]
where [tex]\( k \)[/tex] is the constant of proportionality.
First, we need to determine the value of [tex]\( k \)[/tex]. We are given that [tex]\( y = 24 \)[/tex] when [tex]\( x = 4 \)[/tex].
[tex]\[ 24 = \frac{k}{4} \][/tex]
Solving for k:
[tex]\[ k = 24 \times 4 = 96 \][/tex]
Now that we have the value of [tex]\( k \)[/tex], we can find the value of [tex]\( y \)[/tex] when [tex]\( x = 6 \)[/tex]:
[tex]\[ y = \frac{96}{6} \][/tex]
[tex]\[ y = 16 \][/tex]
**NEEDS TO BE ANSWERED ASAP**
Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.
The following table contains data from a study of two airlines which fly to Small Town, USA.
If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate Airlines flight which was on time.
a. 43/87
b. 43/76
c. 43/48
d. 11/76
Answer: a. [tex]\dfrac{43}{87}[/tex]
Step-by-step explanation:
From the given table , it can be seen that the total number of flights are given : 43+33+6+5=87
Also, the the number of Upstate Airlines flights on time = 43
Now if one of the 87 flights is randomly selected, the probability that the flight selected is an Upstate Airlines flight which was on time will be :-
[tex]\dfrac{\text{Number of Upstate Airlines flight on time}}{\text{Total flight}}\\\\=\dfrac{43}{87}[/tex]
Hence, the probability that the flight selected is an Upstate Airlines flight which was on time [tex]=\dfrac{43}{87}[/tex]
Raul received a score of 72 on a history test for which the class mean was 70 with a standard deviation of 9. he received a score of 71 on a biology test for which the class mean was 70 with standard deviation 7. on which test did he do better relative to the rest of the class?
Final answer:
Raul did better on the history test relative to his classmates, as indicated by a higher z-score of approximately 0.22, compared to 0.14 for the biology test.
Explanation:
To determine on which test Raul did better relative to the rest of the class, we need to calculate the z-scores for Raul's history and biology test results. A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values, measured in terms of standard deviations from the mean. The formula for calculating a z-score is:
z = (X - μ) / σ
where X is the score, μ is the mean, and σ is the standard deviation. Let's apply this to Raul's scores:
For the history test:
z = (72 - 70) / 9 = 2 / 9 ≈ 0.22
For the biology test:
z = (71 - 70) / 7 = 1 / 7 ≈ 0.14
Comparing the two z-scores, we can see that Raul's z-score for history is higher than his z-score for biology. Hence, Raul did better on the history test relative to the rest of the class.
The equation y = 0.75x + 10 describes the cost, y, of placing an ad with x words in the classified section of a newspaper. How many words are in an ad that costs $25?
y = cost = $25
25 = 0.75 +10
subtract 10 from each side
15=0.75x
x = 15/0.75 = 20
there were 20 words in the ad
30% of the 70 buttons had holes how many did not have holes
Find the area. ABCD∼EFGHABCD∼EFGH The area of rectangle ABCD is 72 inches2 and a diagonal is 12 inches. The diagonal of rectangle EFGH is 22 inches. Find the area of rectangle EFGH. Round to the nearest inch2 if necessary.
18.666667 rounded to nearest hundredth
which algebraic expression shows the average melting point of helium hydrogen and neon if h represent melting point of helium, j represent the melting point of hydrogen and K represent the melting point of neon
Answer:
Which algebraic expression shows the average melting points of helium, hydrogen, and neon if h represents the melting point of helium, j represents the melting point of hydrogen, and k represents the melting point of neon?
Step-by-step explanation:
The present value of an ordinary annuity of $350 each year for five years, assuming an opportunity cost of 4 percent, is ________.
The present value of an ordinary annuity of $350 each year for five years with a 4 percent opportunity cost is $1,551.88, calculated using the present value formula for annuities.
To find the present value of an ordinary annuity, you can use the formula for the present value of an annuity:
[tex]\[ PV = Pmt \times \frac{{1 - (1 + r)^{-n}}}{{r}} \][/tex]
Where:
- PV is the present value of the annuity,
- Pmt is the annual payment (in this case, $350),
- r is the interest rate per period (in decimal form),
- n is the number of periods (in this case, 5 years).
Given that the opportunity cost (interest rate) is 4%, or 0.04 in decimal form, and there are 5 years of payments, we can plug these values into the formula:
[tex]\[ PV = 350 \times \frac{{1 - (1 + 0.04)^{-5}}}{{0.04}} \][/tex]
Let's calculate:
[tex]\[ PV = 350 \times \frac{{1 - (1.04)^{-5}}}{{0.04}} \][/tex]
[tex]\[ PV = 350 \times \frac{{1 - (0.8227)}}{{0.04}} \][/tex]
[tex]\[ PV = 350 \times \frac{{0.1773}}{{0.04}} \][/tex]
[tex]\[ PV \approx 350 \times 4.4325 \][/tex]
PV = $1551.88 (Approximately)
So, the present value of the annuity, assuming an opportunity cost of 4%, is approximately $1551.88.
The solution set of 3x+4y<0 lies in which quadrant?
how do i solve this question
if ax +3=7-bx what is x expressed in terms of a and b
Write four hundred seven trillion six million one hundred five thousand twenty eight in standard form
The standard form of four hundred seven trillion six million one hundred five thousand twenty-eight is 407,000,006,105,028.
As we know that,
In trillion, there are 12 zeros.In billion, there are 9 zeros.In million, there are 6 zeros, In thousand, there are 3 zeros.In hundred there are 2 zeros.In tens, there is 1 zero. In ones, there is no zero.So, it should be presented below.
Trillion Billion Million Thousand Hundred Tens Ones
407 , 000 , 006 , 105 , 0 2 8
Therefore we can conclude that the standard form of four hundred seven trillion six million one hundred five thousand twenty-eight is 407,000,006,105,028.
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The area of a rectangle is 52ft ^2 and the length of the rectangle is 5ft less than twice the width. Find the dimensions of the rectangle.
A ball is launched from 8 feet off the ground at an initial vertical speed of 64 feet per second. It is aimed across a field at a target also 8 feet off the ground. The height of the ball at time, t, in seconds, is given by the function, h = –16t 2 + 64t + 8.
what is 10 times as much as 700
tanya set a goal to swim 30 miles over the summer. she plans to swim 3/4 mile per day until she reaches her goal. how many days will it take tanya to reach her goal?
By dividing Tanya's swimming goal of 30 miles by her daily swimming rate of 3/4 mile, we find that it will take her 40 days to reach her goal.
To calculate how many days it will take Tanya to reach her goal of swimming 30 miles by swimming 3/4 mile per day, we need to divide the total goal distance by the daily swimming distance. Therefore, the calculation is as follows:
Divide 30 miles by 3/4 mile.
Since dividing by a fraction is equivalent to multiplying by its reciprocal, we multiply 30 miles by 4/3.
30 miles * 4/3 = 120/3 = 40 days.
Hence, it will take Tanya 40 days to reach her goal of swimming 30 miles if she swims 3/4 mile each day
Write the standard form of the line that passes through the given points.
4, 7) and (0, 7)
The equation of the line would be y = 7 which passes through the points (4, 7) and (0, 7).
What is the slope of the line?The slope of a line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Given that line passes through points (4, 7) and (0, 7)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = 4, y₁ = 7
x₂ = 0, y₂ = 7
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 7 = (7 - 7)/(0- 4)[x -4]
⇒ y - 7 = (0)/(-10 )[x -4]
⇒ y - 7 = 0(x -4)
⇒ y - 7 = 0
⇒ y = 7
Therefore, the equation of the line would be y = 7 which passes through the points (4, 7) and (0, 7).
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How do you rename 805 tens
The volume of a pyramid varies jointly with the base area of the pyramid and its height. The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches. What is the volume of a pyramid with a base area of 10 square inches and a height of 9 inches?
The volume of a pyramid with a base area of 10 square inches and a height of 9 inches will be 30 cubic inches.
What is the volume of the pyramid?Suppose the base of the pyramid has length = L units and width = W units, slant height = K units, and the height of the pyramid is of H units.
Then the volume of the pyramid will be
V = (L × B × H) / 3
V = (Base area x H) / 3
The volume of a pyramid varies jointly with the base area of the pyramid and its height.
The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches.
Then the volume of a pyramid with a base area of 10 square inches and a height of 9 inches will be
V = (10 x 9) / 3
V = 30 cubic inches
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The volume of a pyramid is obtained from the joint variation relationship with its base area and height. Given a certain pyramid's dimensions, we can determine the volume of another pyramid if we know its base area and height. The volume of the second pyramid is 30 cubic inches.
Explanation:The student's question pertains to joint variation, a concept in mathematics, specifically applied here to understand how the volume of a pyramid relates to its base area and height. For a pyramid, this relationship can be expressed as V = k * A * H, where V is volume, A is base area, H is height, and k is the constant of variation.
First, we find the value of 'k' using the given pyramid's measurements; so 24 = k * 24 * 3 gives us k = 1/3.
Then, we use this constant to find the volume of the other pyramid whose base area is 10 square inches and height is 9 inches. Therefore, V = 1/3 * 10 * 9, which simplifies to V = 30 cubic inches.
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Melissa bought a new dishwasher for $1200 the manufacturers offering a 15% rebate how much will the dishwasher cost after the rebate
1200*0.15 = 180
1200-180 = $1020
$1020 after the rebate