Thus, the statement -3 to the -3 power written without using exponents is -1/27.
Explain about the exponents:A number's power or exponent, in other words, tells how many times it must be multiplied by itself. Any integer, fraction, or decimal can serve as the basis in this situation. Moreover, the exponent might have either a positive or negative value.
The exponent rules must be understood while performing mathematical calculations or when simplifying complex equations. There are numerous rules, including the multiplication rule, the rule of negative exponents, and the rule of fractional exponents.Given that-
-3 to the -3 power
This can written as:
= (-3)⁻³
Now using the property of exponents,taking reciprocal of the number will remove the negative number.
= (1 /-3)³
= (1)³ / (-3)³
= 1/(-27)
= - 1/ 27
Thus, the statement -3 to the -3 power written without using exponents is -1/27.
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what is 5x-9 and 3x+9
Answer:
5x - 9 and 3x + 9 are two mathematical expressions. The first expression, 5x - 9, represents a value obtained by multiplying 5 by x and then subtracting 9. The second expression, 3x + 9, represents a value obtained by multiplying 3 by x and then adding 9. Both expressions can be simplified further or used in various mathematical operations depending on the context of the problem or equation in which they are being used.
Answer:-45 and -3
Step-by-step explanation:
Please help with this question A circle is separated into eight sectors of equal area. These eight sectors are arranged to form a shape similar to a parallelogram.
The area of the circle (πr2
) is equal to the area of the parallelogram (bh
).
Select from the drop-down lists to correctly complete each sentence.
The height of the parallelogram is equal to the
of the circle. The base of the parallelogram is equal to
of the circle. Therefore, the area of the circle (πr2
) is equal to the
, and the circumference of the circle is equal to
.
The height of the parallelogram is equal to the diameter of the circle. The base of the parallelogram is equal to half of the circumference of the circle. Therefore, the area of the circle (πr2) is equal to bh and the circumference of the circle is equal to 2b.
The height of the parallelogram is equal to the diameter of the circle. This can be seen because each of the eight sectors has the same area, so they are all the same size. If we place them next to each other in the shape of a parallelogram, we can see that the height of the parallelogram is equal to the diameter of the circle.
The base of the parallelogram is equal to half of the circumference of the circle. This is because the circumference of the circle is divided equally into eight sectors, and the base of the parallelogram is formed by placing two adjacent sectors together. Therefore, the base of the parallelogram is equal to the arc length of one sector plus the arc length of its adjacent sector. Each sector is 1/8th of the circle, so the arc length of one sector is 1/8th of the circumference. Adding the arc lengths of two adjacent sectors gives 1/4th of the circumference, which is half of the base of the parallelogram.
Therefore, the area of the circle (πr2) is equal to the area of the parallelogram (bh), where h is the diameter of the circle and b is half of the circumference of the circle. Additionally, the circumference of the circle is equal to the base of the parallelogram multiplied by 2.
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Who knows how to do thisssssss
I Got U Bro! Answer:(x+5)2+(y+3)2=16
:D
Is a triangle with sides of 5 meters, 12 meters, and 13 meters a right triangle? Explain/Show your work.
Answer:
Step-by-step explanation:
A rectangle has a length of x + 4 cm and a width of 2x − 7 cm.
(a) If the perimeter is 36cm, what is the value of x?
(b) What is the area of this rectangle
Answer:
the value of x is 7
Step-by-step explanation:
First, find the half of the perimeter that is 36 divided by 2 which is 18
Next, write like this
18= l+w( length = width)
which means you have to get the sum of 18
so try sums of 18 randomly like
17 + 1
11 + 7
16+2 etc
but the thing is the value of x must be the same it must not be different so
11 + 7 will be suitable because
11 = 7 + 4
7 = 2 x 7 - 7 = 7
and to find the area which is l x b
11 x 7= 77sq. cm
please mark me the brainliest and a thanks too
Answer:
x=7
Step-by-step explanation:
7+4=11(2)=22
2(7)-7= 14-7= 7(2)=14
22+14=36
What is the probability that either event will occur?
15
A
B
12 18
21
P(A or B)=P(A) + P(B) - P(A and B)
P(A or B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Enter
The probability that either event will occur is given as follows:
P(A or B) = 0.83.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The "or probability" is defined as follows:
P(A or B)=P(A) + P(B) - P(A and B).
From the Venn Diagram, the probabilities of each event are given as follows:
P(A) = 18/(18 + 12 + 6) = 0.5.P(B) = 12/(18 + 12 + 6) = 0.3333.P(A and B) = 0 -> no intersecton.Hence the or probability is given as follows:
P(A or B) = 0.5 + 0.3333 + 0
P(A or B) = 0.83. (rounded to the nearest hundredth).
Missing Information
The Venn diagram is given by the image presented at the end of the answer.
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The diagram below not drawn to scale. Shows a triangle ABC which represent; the cross-section of a roof. BD is the perpendicular to ADC. Calculate the A) length= BD
B) measure of angle CBD
c) area of triangle ABC
d) bearings of B and C
Answer) : B measure of angle CBD
Step-by-step explanation: BD is perpendicular to ADC now we know that there is no scale so all you have to do is measure the length and we gat that answer.
An Internet provider is trying to gain advertising deals and claims that the mean time online per day is than minutes. You are asked to test this claim.
(a) How would you write the null and alternative hypotheses if you represent the Internet provider and want to support the claim?
(b) How would you write the null and alternative hypotheses if you represent a competing advertiser and want to reject the claim?
a. Null hypothesis (H0): The mean time online per day is 30 minutes or more.
Alternative hypothesis (Ha): The mean time online per day is less than or equal to 30 minutes.
b. Null hypothesis (H0): The mean time online per day is less than or equal to 30 minutes.
Alternative hypothesis (Ha): The mean time online per day is more than 30 minutes.
What is null hypothesis?A type of statistical hypothesis known as a "null hypothesis" makes the case that a given set of observations does not have any statistical significance.
A type of statistical hypothesis known as a "null hypothesis" makes the case that a given set of observations does not have any statistical significance.
a) The following is how you can write the null and alternative hypotheses if you are the Internet service provider and want to back up your claim that people spend less than 30 minutes online on average per day:
Null hypothesis (H0): The mean time online per day is 30 minutes or more.
Alternative hypothesis (Ha): The mean time online per day is less than or equal to 30 minutes.
(b)If you address a contending promoter and need to dismiss the case that the interim online each day is not exactly or equivalent to 30 minutes, the invalid and elective speculations can be composed as follows:
Null hypothesis (H0): The mean time online per day is less than or equal to 30 minutes.
Alternative hypothesis (Ha): The mean time online per day is more than 30 minutes.
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Is (-6, 8) a solution to this system of equations?
y = 8
7x + 4y = -10
yes
Or
no
Answer:
7(-6) + 4(8) = -42 + 32 = -10, so (-6, 8) is the solution to this system of equations.
The answer is Yes.
On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the timeframe allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The mean amount of time taken by the students is 23.5 minutes with a standard deviation of 4.8 minutes. The counselor would like to know if the data provide convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes and therefore tests the hypotheses H0: μ = 25 versus Ha: μ < 25, where μ = the true mean amount of time needed by students at this school to complete this portion of the exam. The conditions for inference are met. What are the appropriate test statistic and P-value?
The P-value is between 0.025 and 0.05. and t = -1.85
On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator.
Therefore tests the hypotheses:
[tex]H_0[/tex] : μ = 25 versus Ha: μ < 25,
where μ = the true mean amount of time needed by students at this school to complete this portion of the exam.
The alternative hypothesis is:
[tex]H_1:\mu < 25[/tex]
The test statistic is given by:
[tex]t=\frac{x-\mu}{\frac{s}{\sqrt{n} } }[/tex]
The parameters are:
'x' is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.the values of the parameters are:
x = 23.5 , [tex]\mu=25[/tex] , s = 4.8, n = 35
Plug all the values in above formula of t- statistic is:
[tex]t = \frac{23.5-25}{\frac{4.8}{\sqrt{35} } }[/tex]
t = -1.85
Using a t-distribution , with a left-tailed test, as we are testing if the mean is less than a value and 35 - 1 = 34 df, the p-value is of 0.0365.
t = –1.85; the P-value is between 0.025 and 0.05.
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A right triangle has sides 14 and 48. Use the Pythagorean Theorem to find the length of the hypotenuse.
Answer:
According to the Pythagorean Theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So we have:
c^2 = a^2 + b^2
where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
Substituting the given values, we get:
c^2 = 14^2 + 48^2
c^2 = 196 + 2304
c^2 = 2500
Taking the square root of both sides, we get:
c = 50
Therefore, the length of the hypotenuse is 50 units.
Find the surface area
Round to the nearest tenth
There are [tex]144 + 336 = 480[/tex] square units of surface area overall. The shape has a surface area of 480.0 square units, rounded to the closest tenth.
what is surface area ?The dimensions and shape of the object are taken into account while calculating surface area. The volume of water of a cube, for instance, can be computed by adding the areas of the all six of its equal-sized faces. The surface temperature of something like a sphere, while on the other hand, must be calculated using mathematical methods that take into consideration its radius. The concept of surface area is crucial to many branches of mathematics, science, & engineering.
given
The area of each of the two triangles is [tex](1/2) * 3 * 8 = 12[/tex] square units since each triangle has a base of 3 and a height of 8, respectively.
The trapezium features an 8-inch height, a 6-inch top base, a 12-inch bottom base, and a 10-inch slant height.
two rectangles, each measuring 72 square units: 144 square units (2 x 72)
Four trapezoidal sides, each with a surface area of 12 + 72 = 84 square units 336 square units (4 x 84)
There are [tex]144 + 336 = 480[/tex] square units of surface area overall. The shape has a surface area of 480.0 square units, rounded to the closest tenth.
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Find the error. A student was finding the measure angle 5 in the figure below. She concluded that m angle 5=86
The answer is Option 2: The measure of angle 5 is corresponding to angle 1. Angle 1 is supplementary to 86. So, measure angle 1 = 94. Since corresponding angles are equal angle 5 = 94.
What is a supplementary angle?An angle that, when combined with another angle, creates a straight angle (measuring 180 degrees), is known as a supplementary angle. In other words, if the sum of the measurements of two angles is 180 degrees, they are supplementary. Contrarily, a complimentary angle is one that, when combined with another angle, creates a right angle (which has a 90-degree angle). In other words, if the sum of the measurements of two angles is 90 degrees, they are complimentary. A straight angle and a right angle are not the same thing, hence it is crucial to understand that one angle cannot be both supplementary and complimentary at the same time.
From the given figure we see that the measure of angle 5 is corresponding to angle 1. Angle 1 is supplementary to 86. So, measure angle 1 = 94. Since corresponding angles are equal angle 5 = 94.
Hence, option 2 is correct.
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The complete question is:
Two numbers to have a hcf of 4 one of the numbers is between 10 and 20 and the other is between 20 and 40 what are the two numbers find all possible answers
To find all possible answers, we can start by listing all the numbers between 10 and 20, and all the numbers between 20 and 40, and then check which pairs of numbers have a highest common factor of 4.
Numbers between 10 and 20: 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
Numbers between 20 and 40: 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40
To have a highest common factor of 4, both numbers must be divisible by 4. Therefore, we can eliminate any numbers in these lists that are not divisible by 4.
Numbers between 10 and 20 that are divisible by 4: 12, 16, 20
Numbers between 20 and 40 that are divisible by 4: 20, 24, 28, 32, 36, 40
Now we can check which pairs of these numbers have a highest common factor of 4.
some possible answers are:
12 and 20
12 and 24
12 and 28
12 and 32
12 and 40
16 and 20
16 and 24
16 and 28
16 and 32
16 and 40
20 and 24
20 and 28
20 and 32
20 and 36
20 and 40
there are more answers, all you have to do is to pair 2 numbers.
if you do not want to include 20 and 40 make sure to not chose them.
Hope this could help.
A grain silo can be modeled as a right cylinder topped with a hemisphere. Find the
volume of the silo if it has a height of 31 m and a radius of 5 m. Round your answer to
the nearest tenth if necessary. (Note: diagram is not drawn to scale.)
I hope this helps you.
Use a system of two equations in two variables, and d, to write a formula for the general term (the nth term) of the arithmetic sequence whose fourth term, a4, is 10 and whose sixth term, a6, is 18.
The formula for the nth term of the arithmetic sequence is an = 4n + 2
How to write a formula for the general term (the nth term) of the arithmetic sequence?Let d be the common difference of the arithmetic sequence, and let a1 be the first term. Then we have:
a4 = a1 + 3d = 10
a6 = a1 + 5d = 18
We can solve this system of equations to find a1 and d. Subtracting the first equation from the second, we get:
2d = 8
d = 4
Substituting this into either of the original equations, we get:
a1 + 12 = 18
a1 = 6.
So the arithmetic sequence is:
6, 10, 14, 18, ...
To find the nth term of this sequence, we can use the formula:
an = a1 + (n - 1)d
Substituting in the values of a1 and d, we get:
an = 6 + 4(n - 1)
Simplifying, we get:
an = 4n + 2
Therefore, the formula for the nth term of the arithmetic sequence whose fourth term is 10 and sixth term is 18 is:
an = 4n + 2
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Given A and b to the right, write the augmented matrix for the linear system that corresponds to the matrix equation Axequals
b.
Then solve the system and write the solution as a vector.
Aequals
left bracket Start 3 By 3 Matrix 1st Row 1st Column 1 2nd Column 2 3rd Column negative 3 2nd Row 1st Column negative 3 2nd Column negative 3 3rd Column 3 3rd Row 1st Column 4 2nd Column 2 3rd Column 4 EndMatrix right bracket,
bequals
left bracket Start 3 By 1 Matrix 1st Row 1st Column negative 7 2nd Row 1st Column 15 3rd Row 1st Column negative 4 EndMatrix right bracket
Question content area bottom
Part 1
Write the augmented matrix for the linear system that corresponds to the matrix equation Upper A Bold x equals Bold b
.
The system has the following solution: [tex]x_1=-4,\ x_2=3,\ x_3=1[/tex]. The vector xequals can be used to represent the answer.
What is equation?A statement in mathematics demonstrating the equality of two expressions is called an equation. Two phrases with the same value are normally separated by the equals sign (=). Finding the area of a circle and predicting planetary motion are only two examples of the many practical issues that equations are used to address.
The linear system's augmented matrix, which is determined by the matrix equation A x = b is given by:
Aequals
[tex]\left[\begin{array}{ccc}1&-3&4\\2&-3&2\\-3&3&4\\-7&15&-4\end{array}\right][/tex]
Part 2:
Aequals
Write the system's solution as a vector after solving it.
We can use Gaussian Elimination to solve this system.
Step 1:
[tex]\left[\begin{array}{ccc}1&1&0\\2&-1&1\\-3&0&1\\-7&8&3\end{array}\right][/tex]
Step 2:
Aequals
[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\3&1&0\\-4&3&1\end{array}\right][/tex]
The system's solution is [tex]x_1=-4,\ x_2=3,\ x_3=1[/tex]. The vector xequals represents the answer.
The matrix is,
[tex]\left[\begin{array}{ccc}-4\\3\\1\end{array}\right][/tex]
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Please help me. Giving Brainliest to whoever answers ALL of them!!!
Answer:
First problem:
The correct pairs are 16 and 30, 26 and 38, and 22 and 34.
16 = 2 × 2 × 2 × 2, 30 = 2 × 3 = 5
26 = 2 × 13, 38 = 2 × 19
12 = 2 × 2 × 3, 28 = 2 × 2 × 7
22 = 2 × 11, 34 = 2 × 17
24 = 2 × 2 × 2 × 3,
32 = 2 × 2 × 2 × 2 × 2
gcf(16, 30) = gcf(26, 38) =
gcf(22, 34) = 2
gcf(12, 28) = 4
gcf(24, 32) = 8
Second problem:
f(x) = 3x - 5
f(2) = 3(2) - 5 = 6 - 5 = 1
f(3) = 3(3) - 5 = 9 - 5 = 4
f(4) = 3(4) - 5 = 12 - 5 = 7
f(5) = 3(5) - 5 = 15 - 5 = 10
Hassim's Fireworks & Cycles had free cash flow of R129 550 this year, and expects this to grow by 3% each year for the foreseeable future. The company has a weighted average cost of capital of 8%. What is the value of the company today? 01R 119 186 O2 R 139 914 4. R1 271 945 R2 668 730
Answer:
To calculate the value of Hassim's Fireworks & Cycles today, we can use the formula for the present value of a growing perpetuity:
PV = FCF / (r - g)
where PV is the present value, FCF is the free cash flow, r is the weighted average cost of capital, and g is the growth rate.
Substituting the given values, we get:
PV = 129550 / (0.08 - 0.03)
PV = 2591000
Therefore, the value of Hassim's Fireworks & Cycles today is R2,591,000.
Which of the following equations represents a quadratic function?
a. x=y^2-2y+4
b. y=3x^2-5x+9
c. y=-2x^2+16√x-64
d. -5x+3y=-4
The equation that represents a quadratic function is option b: [tex]y=3x^2-5x+9[/tex]
What is a quadratic function ?
A quadratic function is a function that can be written in the form of f(x) = [tex]ax^2 + bx + c[/tex] , where a, b, and c are constants, and a is not equal to 0. The graph of a quadratic function is a parabola, which can open upwards or downwards, depending on the sign of the coefficient a.
In option b, we can see that the equation is in the form of [tex]f(x) = 3x^2 - 5x + 9[/tex] , which is a quadratic function. The coefficient of [tex]x^2[/tex] is a non-zero constant (a=3), which means that the graph of this function is a parabola.
Option a is not a quadratic function, as it is in the form of [tex]x=y^2-2y+4[/tex], which is a quadratic equation in terms of y, but not in terms of x.
Option c is a little more complicated, as it contains a radical term. However, if we simplify it, we can see that it is also a quadratic function, in terms of x.
Option d is a linear equation, not a quadratic function, because it does not have an [tex]x^2[/tex] term.
Therefore, the quadratic function is [tex]y=3x^2-5x+9[/tex], option b.
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Find the mean, median and mode of the data set. If there is no mode, enter the words "no mode". 72, 65, 68, 68, 73, 45, 68, 71
Answer:
Step-by-step explanation:
72+65+68+68+73+45+68+71 = 530
530/8 because there are 8 numbers
mean: 66.25
for the median, you line the numbers up from small to big and find the center number. But since there are 2 of them (68 and 68) , add 68+68 and divide by 2 which is still 68!
45,65,68,68,68,71,72,73
the mode is 68 because it is the most occurring number.
ok yea
a varies inverselv as b^3. If a =
3/2 when b = 2, find a
when b is 3
If a varies inversely as b³, the value of a when b=3 is 4/9.
Given that, a varies inversely as b³.
Here, a∝1/b³
a=k/b³
Substitute a=3/2 and b=2 in a=k/b³, we get
3/2 = k/2³
3/2 = k/8
3 = k/4
k = 12
Substitute k = 12 in a=k/b³, we get
a=12/b³
When b=3
a = 12/3³
a=12/27
a=4/9
Therefore, if a varies inversely as b³, the value of a when b=3 is 4/9.
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Physicians at a clinic gave what they thought were drugs to 820
patients. Although the doctors later learned that the drugs were really placebos,
52% of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patient's condition improving is .48
Test the hypotheses that the proportion of patients improving is >
.48
We reject the null hypothesis since the p-value is less than the significance level of 0.05.
what is null hypothesis ?The null hypothesis in statistics is a claim that presupposes there is no statistically significant distinction among the two or even more variables be compared. The antithesis of the alternative hypothesis, it is frequently denoted as H0 (Ha). While conducting statistical studies, the null is often evaluated to see if there is sufficient proof against it or not. The default assumption is typically the null hypothesis, and it serves as a benchmark for comparison of the statistical analysis's findings. A statistically significant distinction between the variables under comparison is said to exist if the statistical analysis yields sufficient data to refute a null hypothesis.
given
To test the hypothesis, we can utilise a z-test. This is the test statistic:
[tex]z = (x - E) / σ[/tex]
where x is the observed percentage of patients whose conditions are getting better. x = 820 * 0.52 = 426.4 is the result. Therefore:
z = (426.4 - 393.6) / 0.026 = 1245.98
P(Z > z) = 1 - P(Z z) is the p-value for this one-tailed test, where Z is a normal standard variable. By using a typical table or calculator, we discover:
P(Z > 1245.98) < 0.0001
We reject the null hypothesis since the p-value is less than the significance level of 0.05.
We have enough data to draw the conclusion that the percentage of patients whose conditions are improving is more than 0.48.
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The volume of a cube is increasing at a rate of 56 in∧3/sec. At what rate is the length of each edge of the cube changing when the edges are 6 in. long? (Recall that for a cube,
V = x∧3.)
Answer: The rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.
Step-by-step explanation:
Let's denote the volume of the cube as V and the length of each edge as x. Given that the volume of a cube is V = x^3, we can find the rate at which the length of each edge is changing.
We're given that the rate of change of the volume is dV/dt = 56 in³/sec. We want to find the rate of change of the length of each edge, which is dx/dt, when the length of each edge is 6 inches.
First, we differentiate the volume equation with respect to time t:
V = x^3
dV/dt = d(x^3)/dt
Using the chain rule:
dV/dt = 3x^2 * (dx/dt)
Now, we know that dV/dt = 56 in³/sec and x = 6 in. Plugging these values into the equation, we get:
56 = 3 * (6)^2 * (dx/dt)
Solving for dx/dt:
56 = 108 * (dx/dt)
dx/dt = 56 / 108
dx/dt ≈ 0.5185 in/sec (rounded to four decimal places)
So, the rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.
9x7x9x9x7x9 (I tried the answer 9^4 x 7^2 and it’s not correct
Answer:
321489
Step-by-step explanation:
its for 100 points please
Answer: The first choice.
Step-by-step explanation:
As you can see in the diagram, the line passes through the points[tex](x, y) = (4, -4)[/tex] and [tex](x, y) = (-4, 8)[/tex] . Thus, the slope of the line is [tex]\frac{8-(-4)}{-4-(4)} = \frac{12}{-8} = -\frac{3}{2}.[/tex] Thus, the correct answer is the first choice, as that line has a slope of [tex]-\frac64=-\frac32.[/tex]
An individual depositing in a non-IRA account has to pay income taxes on the funds deposited and on interest earned in each year but does not have to pay taxes on withdrawals from the account.
Sarah, who is five years from retirement, receives a $10,000 bonus at work. She is trying to decide whether to save this extra income in an IRA account or in a regular savings account. Both accounts earn 8 percent nominal interest, and Sarah is in the 30 percent tax bracket in every year (including her retirement year)
If Sarah invests in the normal savings account, her net value (after taxes) five years from now will be?:
The net value of the $10,000 bonus in a normal savings account after taxes and interest in five years will be $9,181.
What is the net value of Sarah's $10,000 bonus in a normal savings account after taxes and interest in five years?Assuming an 8 percent nominal interest rate and a 30 percent tax bracket, the after-tax return on the normal savings account is 5.6 percent. Thus, after five years, the $10,000 bonus will grow to $14,693.
However, since Sarah is in the 30 percent tax bracket in every year, she will owe taxes on the interest income earned each year. This reduces the after-tax return to 3.92 percent. Therefore, in five years, the $10,000 bonus in the normal savings account will be worth $9,181 after taxes.
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A sociologist polled a random sample of people and asked them their age and annual income. The two-way frequency table below shows the results.
Annual income vs. age group
Less than
$
50
,
000
$50,000dollar sign, 50, comma, 000 At least
$
50
,
000
$50,000dollar sign, 50, comma, 000 Total
Ages
44
4444 and under
148
148148
68
6868
216
216216
Ages
45
4545 and above
38
3838
94
9494
132
132132
Total
186
186186
162
162162
348
348348
Which of the following statements is true of those polled?
According to the information, we can infer that the correct sentences about the graph is A person with annual income of at least $50,000 is more likely to be 45 years old or above.
How to find the correct sentence?To find the correct sentence we have to analyze the information of the graph and read the options. Once we make this procedure, we can compare each sentence with the information of the graph to establish the correct one.
According to the information the correct option would be A person with annual income of at least $50,000 is more likely to be 45 years old or above (option C).
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Working together, Mike and Stephanie can wash a car in 8.24 minutes. Had she done it alone it would have taken Stephanie 17 minutes. How long would it take Mike to do it alone?
It would take Mike approximately 0.989 minutes (or about 59 seconds) to wash the car alone.
We have,
Let's start by assigning variables to unknown quantities.
Let m be the time it takes for Mike to wash the car alone (in minutes).
We know that Stephanie takes 17 minutes to wash the car alone, so her rate of work is 1/17 car per minute.
Working together, their combined rate of work is 1/8.24 car per minute.
Using the formula:
(rate of work) = (amount of work) / (time)
we can set up the following equation to represent the work they do together:
1/8.24 = (1 car) / t
where t is the time it takes them to wash the car together.
We can also set up a similar equation for Stephanie's work alone:
1/17 = (1 car) / (t + x)
where x is the extra time it takes Mike to wash the car alone.
Since they are working on the same car, the amount of work done in both cases is the same, so we can set the two equations equal to each other and solve for x:
1/8.24 = 1/(t + x) + 1/17
Multiplying both sides by the least common multiple of the denominators (8.2417(t+x)).
17*(t+x) + 8.24*(t+x) = 8.24*17
Simplifying.
25.24t + 17x = 139.68
We also know that Mike's rate of work is 1/m car per minute.
Since we know the combined rate of work when they work together, we can set up another equation:
1/m + 1/17 = 1/8.24
Multiplying both sides by the least common multiple of the denominators (8.2417m).
178.24m + 8.2417m = 8.2417m + m8.24m
Simplifying.
141.08m = 139.68
Solving for m.
m = 0.989
Therefore,
It would take Mike approximately 0.989 minutes (or about 59 seconds) to wash the car alone.
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Select the expression that represents this real-world situation.
There are p people on the bus. At the next stop, 8 people get off and 5 more get on. Write an expression to show how many people are on the bus.
p − 8 + 5
p + 8 − 5
p x (8 + 5)
p ÷ (8 − 5)
The expression that represents the real-world situation is "p - 8 + 5". It simplifies to "p - 3" and represents the final number of people on the bus.
What is an expression?An expression is a combination of numbers, symbols, and/or operators that represents a quantity, a value, or a computation. Expressions can include variables, which are letters that represent unknown values, and can be manipulated and evaluated using mathematical operations like addition, subtraction, multiplication, and division. Expressions can be simple or complex, and they are used in various areas of mathematics, including algebra, calculus, and geometry, as well as in many other fields such as physics, engineering, and economics.
According to the given information:The expression that represents the real-world situation is:
p - 8 + 5
Explanation:
Initially, there are p people on the bus. Then, 8 people get off, which is represented by the subtraction of 8 from p (p - 8). After that, 5 more people get on the bus, which is represented by adding 5 to p - 8, giving us the final expression: p - 8 + 5. This expression simplifies to p - 3, which represents the final number of people on the bus.
Therefore, The expression that represents the real-world situation is "p - 8 + 5". It simplifies to "p - 3" and represents the final number of people on the bus.
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