Need help! Due very soon
a) Complete the prime factor trees for 24 and 40:
24
2
2
6
2
40
2
2
3
b) What is the Lowest Common Multiple of 24 and 40?
2
2
1
5
Submit Answer
Answer:
a)
24 = 2³ × 3
40 = 2³ × 5
b)
LCM = 120
Step-by-step explanation:
a)
24 40
/ \ / \
2 12 2 20
/ \ / \
2 6 2 10
/ \ / \
2 3 2 5
24 = 2³ × 3
40 = 2³ × 5
b)
LCM = 2³ × 3 × 5
LCM = 120
Find the length of the third side. If necessary, round to the nearest tenth
Answer: 26
Step-by-step explanation:
In the picture, we are given a right triangle. Based on that, we can use the Pythagorean Theorem, which helps us find the missing side length with the formula [tex]a^2+b^2=c^2[/tex].
a and b represent the legs, and c is the hypotenuse. The hypotenuse is the longest side of the right triangle. It is also the side that is diagonal from the right angle.
In the picture, we are presented with the legs. So, we can plug in the legs into a and b to solve for c.
[tex]a^2+b^2=c^2[/tex] [plug in a and b]
[tex]10^2+24^2=c^2[/tex] [exponent]
[tex]100+576=c^2[/tex] [add]
[tex]676=c^2[/tex] [square root both sides]
[tex]c=26[/tex]
This tells us that the length of the third side is 26.
determine whether 3y - 7 = 2x -7 represents direct variation or not. If it does, find the
constant of variation.
Answer:
Yes, it represents direct variation.
The constant of variation is 2/3.
Step-by-step explanation:
Rearrange the equation to put it into y = kx form, which is the direct variation equation
3y - 7 = 2x - 7
Add 7 to both sides:
3y - 7 = 2x - 7
3y = 2x
Divide each side by 3:
y = 2/3x
So, the equation is y = 2/3x, which represents direct variation because it is in the form y = kx.
In y = kx, k is the constant of variation. Since the equation is y = 2/3x, k = 2/3.
So, the constant of variation is 2/3.
A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains $100$ cans, how many rows does it contain
A grocer makes a display of cans in which there are 10 rows.
The top row has one can and each lower row has two more cans than the row above it.
We can write it as sequence:
1, 3, 5, 7, . . .
We can observe that it's an arithmetic sequence: 1, 3, 5, 7, . . . , 2n-1
We know that the formula for the sum of n-terms of arithmetic sequence:
S(n) = (n/2)(1 + 2n-1)
Here, Sn = 100
So, (n/2)[1 + 2n-1] = 100
n(1 + 2n + 1)
n(2n) = 200
2n^2 = 200
n^2 = 100
n = 10
Hence, the number of rows = 10
Learn more about the sequence here:
https://brainly.com/question/12429779
#SPJ4
Using traditional methods it takes 8.5 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 21 students and observed that they had a mean of 8.8 hours with a variance of 1.21 . Is there evidence at the 0.05 level that the technique performs differently than the traditional method? Assume the population distribution is approximately normal. Step 1 of 5 : State the null and alternative hypotheses
As the p-value of the test is of 0.215 > 0.05, there is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.
What are the null and the alternative hypothesis?At the null hypothesis, it is tested if there is no evidence of different performance, that is, the mean is of 8.5 hours, hence:
[tex]H_0: \mu = 8.5[/tex]
At the alternative hypothesis, it is tested if there is evidence of different performance, with a mean different of 8.5 hours, hence:
[tex]H_1: \mu \neq 8.5[/tex]
What is the test statistic?The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.
The equation is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are given as follows:
[tex]\overline{x} = 8.8, \mu = 8.5, \sigma = \sqrt{1.21} = 1.1, n = 21[/tex]
Hence the test statistic is calculated as follows:
[tex]z = \frac{8.8 - 8.5}{\frac{1.1}{\sqrt{21}}}[/tex]
z = (8.8 - 8.5)/(1.11/square root of 21)
z = 1.24.
What is the p-value and conclusion?The p-value is obtained using a z-distribution calculator.
We have a two-tailed test, as we are testing if the mean is different of a value, with a test statistic of z = 1.24, hence the p-value is of:
0.215.
(2 multiplied by the subtraction of one and the p-value of z = 1.24).
The p-value is greater than the significance level of 0.05, meaning that there is not enough evidence to reject the null hypothesis and conclude that there is a difference between the two methods.
More can be learned about the test of an hypothesis at https://brainly.com/question/13873630
#SPJ1
The length of some material is 8.3m correct to 2 significant figures. Write the error int
length, x, of the material.
Therefore , the solution of the given problem of equation comes out to be the error range for x is [1250, 1350].
Explain the equation.A mathematical equation is a formula that uses the equal sign (=) to connect two statements and express equality. A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The equal sign is a crucial part of mathematical formulas, especially equations. Algebra is frequently utilized in equations. Algebra is used in mathematics when it is difficult to determine a precise quantity.
Here,
Given: Some material has a length of 8.3 meters
We have provided a number, x, that has been rounded to two significant numbers with the supplied error.
Next, we must determine the x error interval.
It is necessary for x to have a value that is both bigger than or equal to 1250 and less than or equal to 1300.
i.e.,1250 ≤ x ≤ 1300 ---(1)
2. The value of x is more than 1300 but not equal to 1350.
1300 ≤ x ≤ 1350--- (2)
When (1) and (2) are combined, we obtain
1250≤ x ≤ 1350
As a result, 1350 is not part of the error-interval for x.
As a result, the interval notation is [1250, 1350].
As a result, the error range for x is [1250, 1350].
Therefore , the solution of the given problem of equation comes out to be the error range for x is [1250, 1350].
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
a circle has a radius of 6 inches and a central angle of 60°. What is the measure of the arc length associated with this angle
3pi inches
2pi inches
pi inches
6pi inches
Answer:
Option B. 2π inches
Step-by-step explanation:
From the question given above, the following data were obtained:
Radius (r) = 6 in
Centre angle (θ) = 60 °
Length of arc (L) =?
The length of arc can be obtained as follow:
L = 2πr × (θ/360°)
L = 2 × 6 × π × (60/360)
L = 12π × 1/6
L = 2π in
Thus, the length of the arc is 2π in.
what is the value of z? (multiple choice)
Which expression is equivalent to
4x + ?
o 1(-x+2)
o 1(-2+ 3)
-1(-x+ )
- (x + 2)
Answer:
Definitely Option A.
When you expand the bracket of Option A... You have your equation
Which is
-1/4x + 1/2.
PLEASE HELP I will give brainiest Which equation best shows the relationship between x and y? (1 point)
O a
Ob
Oc
Od
y = x + 50
y = 6x + 50
y = 6x + 56
y=x+56
On solving the provided question, we can say that the equation of the expression is given by y = 6x + 50
What is an equation ?Equations with graphs as the unknowns are known as graph equations. The concept of isomorphism is one of the key issues in graph theory. When are two graphs identical, we inquire? Different graph equations may be used to express the aforementioned graphs.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is utilized. A lot of specialists, such as air traffic controllers, architects, computer programmers, and carpenters, employ equations on a daily basis.
From the table we can see that if the equation be
y = mx + c
for x = 0 y = 50
c = 50
again from x = 1 and y = 56
m = 6
So the equation of the expression is given by y = 6x + 50
To know more about Equation visit:
brainly.com/question/28896968
#SPJ1
An object is moving at a speed of 11 yards every 6 months. Express this speed in centimeters per hour.
Speed of the given object in centimeters per hour
= 0.23 cm / hour
What is unit conversion?Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters.
Like 1 yard = 91.44 cm
1 month = 730 hrs.
Distance covered by the object = 11 yards
Distance covered in cm = 11 × 91.44 = 1005.84 cm
Time taken to cover 11 yards = 6 months
Time taken in hours = 6 × 730 = 4380 hrs.
Speed of the object = distance covered by the object / Time taken
Speed of the object = 1005.84/4380 = 0.2296 ≈ 0.23 cm per hour
Hence, in centimeters per hour,
the speed of the object is 0.23 cm / hour.
Learn more about unit conversion here:
https://brainly.com/question/7171227
#SPJ1
Claire buys a new car for £5700.
She pays a deposit of 12%
She then pays the rest of the cost in 15 equal monthly payments.
How much is each monthly payment
Answer:
$334.40
Step-by-step explanation:
Find how much she has left to pay after the deposit:
Multiply 5700 by 0.88
5700(0.88)
= 5016
Divide this by 15 to find how much each monthly payment is:
5016/15
= 334.4
So, each monthly payment is $334.40
Given that AB is a line segment and the angle
y
= 33°, work out the value of the angle marked
x
.
180-33
=147
so X= 147
FROM CAMBRIDGE UNIVERSITY!
1. To find members for her skate team, Heather prints flyers to display around town. She posts 6 flyers
at her school and f flyers at each of the 3 nearest skate parks. Write two different expressions that
represent the total number of flyers posted.
Find the total number of flyers posted if f= 5.
Recently, the Town of Aberdeen announced they were going to acquire a large parcel of land for a new park initiative.
What is piecewise function?To fully understand what piecewise functions are and how we can construct our own piecewise-defined functions, let’s first dive into a deeper understanding of how it works.A piecewise function is a function that is defined by different formulas or functions for each given interval. It’s also in the name: piece. The function is defined by pieces of functions for each part of the domain.In mathematics, a piecewise-defined function is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain. Piecewise definition is actually a way of expressing the function, rather than a characteristic of the function itself.To learn more about piecewise function refer to:
https://brainly.com/question/27262465
#SPJ1
can someone help me
Answer:
y=-1/4x+2
Step-by-step explanation:
Answer:
Step-by-step explanation:
add all the # and see what you get
Please help ASAP!
Solve the inequities:
k^2-7k+12. 25>0
2. 25y^2-3y+1<0
It is not possible to mix ‘greater than’ and ‘less than’ inequality signs in the same expression
Solve the inequities:
k^2-7k+12. 25>0
2. 25y^2-3y+1<0
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
It is not possible to mix ‘greater than’ and ‘less than’ inequality signs in the same expression
So Whenever you find two conclusions which are false Just check for these two symbols . In Most of the case where two conclusions are false and these two signs are not there respectively than that statement, you can call it as Neither Nor.
To know more about inequalities visit brainly.com/question/28823603
#SPJ4
What is the area of this parallelogram?
Answer: B
Step-by-step explanation:
Area = 4 x 5
= 20 cm^2
Remember that area of parallelogram is the base x perpendicular height. is The perpendicular height is not 6cm but 5cm. (right angle labelled on diagram)
Answer: 20 cm²
Step-by-step explanation:
area parallelogram = base x height
=> 4 x 5 = 20
Write an expression for the calculation double the product of 5 and 9.
Answer:
2 (5×9)
Step-by-step explanation:
the product of 5 and 9 is DOUBLED. so the calculation will be 2 times 5×9
PLEASE HELP!! Puzzle One
Determine the volume of the following cylinders with the given dimensions. To break
the code substitute your answers in for the correct letters. Make sure to follow the
order of operations! Round your answers to the hundredth place. Use 3.14 for an
approximation for pi.
The volume of the cylinders are 320.625 m³, 921.6 ft³,824 in³ and 35.6 in³
How to calculate volume?Volume is the amount of space occupied by a three dimensional shape or object.
Volume of cylinder = π * radius² * height
a) Volume of cylinder = π * (15/2)² * 5.7 = 320.625 m³
b) Volume of cylinder = π * (8)² * 14.4 = 921.6 ft³
c) Volume of cylinder = π * (6)² * 24 = 824 in³
d) Volume of cylinder = π * (2)² * 8.9 = 35.6 in³
The volume of the cylinders are 320.625 m³, 921.6 ft³,824 in³ and 35.6 in³
Find out more on volume at: https://brainly.com/question/1972490
7O POINTS HELP ASAP!!!
Given the graph of this function, determine the statement that best describes the end behavior.
x->∞,y->∞ and as x-> - ∞ , y-> - ∞ this statement best describes the end behavior.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
First, we need to analyze the plotting of the graph. When it is on the negative axis of x, as the values of x increase (x values increasing in the negative axis means it's decreasing in value), the y values also increase. So as x decreases, y increases.
On the positive axis of x, as the x values increase, the corresponding values of y also increase with x. So as x increases, y values also increase with it.
Hence, x->∞,y->∞ and as x-> - ∞ , y-> - ∞ this statement best describes the end behavior.
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ1
Pepito bought 2 t-shirt at 149.95 each and a pair of pants for php 30.75, if her money was a 200 pesos bill. How much was her change?
If pesos had it would be so pesos have 169.25 dollars left 200-30.75=169.25
a company spent 762500 to make a movie that will be shown in theaters for 8 weeks. If the movie makes 1250000 in its first week how much money does the movie need to earn in the next 7 weeks to make profit of atleast 2,000,000
The movie need to earn $ 1,512,500 in the next 7 weeks.
What is Unitary Method?The unitary technique involves first determining the value of a single unit,
followed by the value of the necessary number of units.
For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
A company spent 762500 to make a movie.
The total movie will be earned
= 762500 + 2000000
= 2,762,500
First week the movie earned 1, 250,000.
So, in 7 weeks the movie needs to earned
= 2,762,500 - 1, 250,000
= 1,512,500
Hence, the movie earn 1,512,500 more.
Learn more about Unitary Method here:
https://brainly.com/question/22056199
#SPJ1
please help i dont understand this
Answer:
Equation is 7x^2 – 5x + 2
comparing with a,b and c
a = 7
b= –5
c = 2
Is 2x 3 5 is a linear equation?
yes, 2x + 3 = 5 is a linear equation.
What is a linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." If a linear equation contains two variables, it is referred to as a linear equation in two variables, and so on.
Non-linear equations are those that do not produce a straight line. It has a changeable slope value and resembles a graphed curve.
Given that,
2x + 3 = 5
or, 2x = 5 - 3
or, 2x = 2
or, x = 2/2
x = 1
To know more about linear equation refer to:
https://brainly.com/question/12788590
#SPJ4
identify the initial amount a and the growth factor b in the exponential function: f(X) = 610 • 7.54
The initial amount is 610 and the growth factor is 7.54.
What is an exponential function?
An exponential function has the form f(x) = a*b^x, where a is the initial amount, also called the y-intercept, and b is the growth factor.
In the function f(X) = 610 • 7.54, the initial amount is a = 610, and the growth factor is b = 7.54.
Hence, the initial amount is 610 and the growth factor is 7.54.
To learn more about the exponential function, visit:
https://brainly.com/question/2456547
#SPJ1
The initial amount is 610 and the growth factor is 7.54.
What is an exponential function?An exponential function has the form f(x) = a*b^x, where a is the initial amount, also called the y-intercept, and b is the growth factor.
What is growth factor?A growth factor is a naturally occurring substance that stimulates a cell to grow, divide, and differentiate. Growth factors are typically proteins or peptides that bind to specific receptors on the surface of cells, triggering signaling pathways that lead to cell proliferation and survival.
In the function f(X) = 610 • 7.54, the initial amount is a = 610, and the growth factor is b = 7.54.
Hence, the initial amount is 610 and the growth factor is 7.54.
To learn more about the exponential function, visit:
brainly.com/question/2456547
#SPJ1
Which expression can be written as
[tex]k \sqrt{3} [/tex]where k is an integer?
a.
[tex] \sqrt{63} [/tex]
b.
[tex] \sqrt{108} [/tex]
c.
[tex] \sqrt{144} [/tex]
d.
[tex] \sqrt{150} [/tex]
Answer:
B. [tex] \sqrt{108} [/tex]
Step-by-step explanation:
The simplified forms of these roots are :
A. [tex] \sqrt{63} [/tex] = [tex]3 \sqrt{7} [/tex]
B. [tex] \sqrt{108} [/tex] = [tex]6 \sqrt{3} [/tex]
C. [tex] \sqrt{144} [/tex] = [tex]3 \sqrt{286} [/tex]
D. [tex] \sqrt{150} [/tex] = [tex]5 \sqrt{6} [/tex]
Check:
[tex] \sqrt{108} [/tex]
[tex] \sqrt{36(3)} [/tex]
[tex] \sqrt{ {6}^{2} \times 3} [/tex]
[tex]6 \sqrt{3} [/tex]
Hope it is helpful...SEVENTH GRADE ALGEBRA PLS HELP
A group of 5 friends each have x action figures in their collections. Each
friend buys 8 more action figures. Now the 5 friends have a total of 150
action figures.
Write an equation that can be used to find x, the number of action
figures per person.
Answer:
x = 22 (each friend started with 22 action figures)
Step-by-step explanation:
After buying 8 more action figures, each friend has x + 8 action figures. Because there are 5 friends, the new total number of action figures is 5(x + 8), which we are told is equal to 150. Dividing both sides of this equation by 5 yields x + 8 = 30, and subtracting 8 from both sides yields x = 22.
In ΔNOP, n = 89 cm, p = 36 cm and ∠P=147°. Find all possible values of ∠N, to the nearest 10th of a degree.
Answer: No Possible Triangles
Step-by-step explanation: DeltaMath
Just hit the enter button, don’t type anything in the box or else it will mark it wrong.
An achievement exam was given to a population of 1,000 students. However, a sample of only seven of student scores is listed along with their respective z score and percentile rank in the following table. TEST SCORE 42 57 67 72 77 87 97 z score -1.50 -0.75 -0.25 0 0.25 0.75 1.25 percentile rank 10 25 30 45 50 75 95 Using the table information, the test score representing the 3rd decile is: a. 67 b. 77 c. 57 d. 72 e. 97
The test score representing the 3rd decile is 67. So the option a is correct.
In the given question, an achievement exam was given to a population of 1,000 students.
However, a sample of only seven of student scores is listed along with their respective z score and percentile rank in the following table.
TEST SCORE 42 57 67 72 77 87 97
z score -1.50 -0.75 -0.25 0 0.25 0.75 1.25
percentile rank 10 25 30 45 50 75 95
Using the table information, we have to find the test score representing the 3rd decile.
As we know that the 3rd decile is equal to the 30th percentile.
So that the 3rd decile have the percentile rank = 30
The test score equivalent to percentile rank 30 is 67.
So, the test score representing the 3rd decile is 67. So the option a is correct.
To learn more about percentile rank link is here
brainly.com/question/27872151
#SPJ4