Answer:
Step-by-step explanation:
155
The number of boxes required by the school to order is 155.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We have been given that the school needs 1,860 pencils for its students. Also, the pencils are sold in boxes of 12.
We need to find the school needs to requires boxes to order.
Total number of pencil = 1,860
Number of boxes = 12
Therefore, boxes needed = 1,860 / 12
= 155
Hence, the number of boxes required by the school to order is 155.
To learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ5
Solve for x. e^x - e ^ -x / e^x + e ^-x = t
Answer:
D
Step-by-step explanation:
(eˣ − e⁻ˣ) / (eˣ + e⁻ˣ) = t
Multiply by eˣ/eˣ.
(e²ˣ − 1) / (e²ˣ + 1) = t
Solve for e²ˣ.
e²ˣ − 1 = (e²ˣ + 1) t
e²ˣ − 1 = e²ˣ t + t
e²ˣ = 1 + e²ˣ t + t
e²ˣ − e²ˣ t = 1 + t
e²ˣ (1 − t) = 1 + t
e²ˣ = (1 + t) / (1 − t)
Solve for x.
2x = ln[(1 + t) / (1 − t)]
x = ½ ln[(1 + t) / (1 − t)]
Use log rule.
x = ln(√[(1 + t) / (1 − t)])
select the statements and number line that can represent the inequality.
Answer:
every equivalent to 6 ≤ x
Step-by-step explanation:
We can subtract 5+11/6x to get ...
7 ≤ -(11/6)x +3x = (7/6)x
Multiplying by 6/7 gives ...
6 ≤ x
__
When x is in the set of real numbers, x in any real number that is 6 or more.
When x is in the set of integers, x is any integer that is 6 or more: {6, 7, 8, ...}.
When no set is specified, the solution is simply ...
6 ≤ x
Antoinette needs to solve this system of equations by graphing. Which statements explain how she should graph the equations? Check all that apply.
Answer:
see below
Step-by-step explanation:
In my opinion, Antoinette should make use of a graphing calculator to find the solution. (second attachment)
__
Slope-intercept form can be useful for graphing, so it often works well to start with equations in that form. If that is Antoinette's strategy, she should rewrite the first equation to that form. The second equation is already in slope-intercept form.
In doing that rewrite, she will want to get the y-term on one side of the equal sign by itself. She can do that by subtracting 2x from the first equation:
-7y = -2x +56
As a final step in her rewrite, she would divide by -7 to get ...
y = 2/7x +56
This 2nd equation has a positive slope of 2/7. The slope of the second equation is similarly the x-coefficient, -2.5. Neither is 4 and they have different signs.
The appropriate answer choices are shown checked below.
Answer:
B and D
Step-by-step explanation:
I got it right m8. Good day
Please help me with this question, I need it to pass the class!!
Answer:
cos(20°)
Step-by-step explanation:
The "cofunction" is the function having the same value for the complement of the angle that this function has for the angle.
The cofunction of sine is cosine. The complement of 70° is 90° -70° = 20°.
sin(70°) = cos(20°)
An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you that the printing speed is actually a Normal random variable with a mean of 17.48 ppm and a standard deviation of 3.25 ppm. Suppose that you draw a random sample of 10 printers.
Using the information about the distribution of the printing speeds given by the manufacturer, find the probability that the mean printing speed of the sample is greater than 18.06 ppm. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places). Probability (as a proportion)
Answer:
0.288
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 17.48, \sigma = 3.25, n = 10, s = \frac{3.25}{\sqrt{10}} = 1.027740[/tex]
Find the probability that the mean printing speed of the sample is greater than 18.06 ppm.
This is 1 subtracted by the pvalue of Z when X = 18.06. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{18.06 - 17.48}{1.027740}[/tex]
[tex]Z = 0.56[/tex]
[tex]Z = 0.56[/tex] has a pvalue of 0.712
1 - 0.712 = 0.288
The answer is 0.288
Solve the following absolute value equation:
|2x-5|=7
x= -6 or x = 1
x = 6 or x = 1
x= -6 or x= -1
x = 6 or x= -1
Answer:
x = 6 x = -1
Step-by-step explanation:
When we have absolute value equations, we get two solutions, one positive and one negative
2x - 5 =7 2x -5= -7
Add 5 to each side
2x-5+5 = 7+5 2x -5+5 = -7+5
2x =12 2x = -2
Divide each side by 2
2x/2 =12/2 2x/2 = -2/2
x = 6 x = -1
The image point using the translation (x,) + (x+4,y-1)
for the point (3,3) is
Answer: (7, 2)
Step-by-step explanation:
(x, y) → (x + 4, y - 1)
(3, 3) → (3 + 4, 3 - 1)
= (7, 2)
What is the area of the circle?
Answer:
A =50.24 in ^2
Step-by-step explanation:
The diameter is 8 inches
The radius is 1/2 diameter
r = d/2 = 8/2 = 4
The area of the circle is given by
A = pi r^2
A = 3.14 (4)^2
A =50.24 in ^2
Answer:
C. 50.24 in²
Step-by-step explanation:
d= 8 in
r= 8/2= 4 in
Area= πr²= 3.14×4²= 50.24 in²
Gordon Miller's job shop has four work areas, A, B, C, and D. Distances in feet between centers of the work areas are: A B C D A − 5 9 7 B − − 6 8 C − − − 11 D − − − − Workpieces moved per week between work areas are: A B C D A − 900 900 500 B − − 500 200 C − − − 600 D − − − − It costs Gordon $22 to move 1 work piece 1 foot.What is the weekly total material handling cost of the layout?
Answer: $600,600
Step-by-step explanation:
Total handling cost :
Workpiece moved * cost * distance
Work area A :
-, (5 × 22 × 900), (9 × 22 × 900), (7 × 22 × 500)
-, 99000, 178200, 77000
Work area B:
-, -, (6 × 22 × 500), (8 × 22 × 200)
-, -, 66000, 35200
Work area C:
-, -, -, (11 × 22 × 600)
-,-,-, 145200
Work area D:
-, -, -, -
Total weekly handling cost :
(99000 + 178200 + 77000 + 66000 + 35200 + 145200)
= $600,600
Kindly check attached picture for more explanation
If the point (7,6) lies on the graph of y = (x - 5)2 + k, where k is some constant, which other point must also
lie on the same graph?
Answer:
k = -4 (0, -14) also lies on the graph
Step-by-step explanation:
6 = (7 - 2)2 + k
6 = 10 + k
-4 = k
y = (0 - 5)2 - 4, y = -14
which of the points shown below are on the line given by the equation y=3x?check all that apply.
Point A: (1,3)
Point B: (3,1)
Point C: (3,-1)
Point D: (-1,-3)
Answer:
Point A: (1,3)Point D: (-1,-3)Step-by-step explanation:
The value of y in the (x, y) pair must be 3 times the value of x if the point is to be on the line. That is the case for points A, D.
A soccer league has 180 players. Of those players 50% are boys. How many boys are in the soccer league?
Answer:
90 boys
Step-by-step explanation:
There are 180 players
Multiply by the percent that are boys to find the number of boys
180 * 50%
180 * .50
90
Answer:
90 boys
Step-by-step explanation:
The soccer league has 180 players, and 50% or half are boys.
Multiply the total number of players in the league by the percent that are boys.
total number of players * percent of boys
180* 50%
Convert 50% to a decimal by dividing by 100, or moving the decimal place 2 spaces to the left.
50/100=0.50
50.0–>5.0–>0.50
180*0.50
Multiply
90
There are 90 boy soccer players in the league.
what are the answers to the following quadratic equation:
x^2-4x-12
Answer:
6 and -2
Step-by-step explanation:
x^2-4x-12
set up equal to zero
x^2-4x-12=0
lets factor:
(x-6)(x+2)=0
x-6=0
x=6
or
x+2=0
x=-2
Answer:
x=6 x=-2
Step-by-step explanation:
x^2-4x-12 = 0
Factor
What two numbers multiply to -12 and add to -4
-6*2 = -12
-6+2 = -4
(x-6)(x+2) =0
Using the zero product property
(x-6) =0 x+2 = 0
x=6 x=-2
What is the square root of x if x = 25?
Answer:
5 is your answer
Step-by-step explanation:
The [tex]\sqrt{25}[/tex] will equal to 5, because [tex]5^2[/tex] = 25
Answer:
5
Step-by-step explanation:
5 x 5 =25, so it is the square root of 25
In a recent survey, 10 percent of the participants rated Pepsi as being "concerned with my health." PepsiCo's response included a new "Smart Spot" symbol on its products that meet certain nutrition criteria, to help consumers who seek more healthful eating options. Suppose a follow-up survey shows that 18 of 100 persons now rate Pepsi as being "concerned with my health". Calculate the z statistic. (Round your answer to 2 decimal places.) zcalc At α = .05, would a follow-up survey showing that 18 of 100 persons now rate Pepsi as being "concerned with my health" provide sufficient evidence that the percentage has increased? Yes No
Answer: What what my you explain shorter please
Step-by-step explanation:
Write two trinomials that you can factor into two binomials. Factor each trinomial. Then write one trinomial that you cannot factor and explain why.
Answer:
- Trinomials that can be factored into two binomials are:
1. x² + 5x + 6
Factored to: (x + 3)(x + 2)
2. x² + x - 2
Factored to: (x - 1)(x + 2)
Example of a Trinomial that cannot be factored into two binomials:
x² + 5x + 1
Step-by-step explanation:
- A trinomial is a polynomial that consist of three terms. It is in the form:
ax² + bx + c.
- A binomial is a polynomial that consists of two terms. It is of the form:
bx + c.
A trinomial is said to be factorable if the can be written as a product of two binomials.
Example 1:
The expression: x² + 5x + 6
Can be rewritten as:
x² + 2x + 3x + 6
Grouping this, we have
(x² + 2x) + (3x + 6)
Which becomes
x(x + 2) + 3(x + 2)
Factoring (x + 2), we have
(x + 3)(x + 2)
Which is a product of two binomials as required.
Therefore, the expression is factorable.
Example 2:
The trinomial expression:
x² + x - 2
Can be written as:
x² + 2x - x - 2
= (x² + 2x) - (x + 2)
= x(x + 2) - (x + 2)
Factoring (x + 2), we have
(x - 1)(x + 2)
This a product of two binomials, hence, the tutorial is factorable.
Example 3:
Consider the trinomial:
x² + 5x + 1
This is not factorable, because the term 5x cannot be split into a sum or difference, in such a way that it has a common factor with x² and with 1.
Unlike in the case of Example 1.
x² + 5x + 6
5x was split into the sum of 2x and 3x
That is, x² + 5x + 6 = x² + 2x + 3x + 6
So that, 2x has a common factor, x with x², and 3x has a common factor, 3 with 6.
The square of a number is 12 less than 7 times the number.what is the number?
Answer:
n = 3 or n = 4
Step-by-step explanation:
Let the unknown number be n.
Then:
n² = 7n - 12
In standard quadratic form, we have:
n² - 7n + 12 = 0
In factored form, we have:
(n - 3)(n - 4) = 0, and so
n = 3 and n = 4
A tree casts an 8-foot shadow on the ground. The length from the tip of the shadow to the top of the tree is 17 feet. What is the height of the tree?
Answer:
Height of tree = 15 ft
Step-by-step explanation:
Given:
Length of shadow (Base) = 8 ft
Length from the tip to top of the tree (Hypotenues) = 17 ft
Find:
Height of tree = ?
Computation:
Using Pythagoras theorem:
[tex]Height\ of\ tree = \sqrt{Hypotenues^2 - base^2} \\\\Height\ of\ tree = \sqrt{17^2 - 8^2} \\\\Height\ of\ tree = \sqrt{289-64}\\\\Height\ of\ tree = \sqrt{225}\\\\ Height\ of\ tree =15[/tex]
Height of tree = 15 ft
Answer:
The answer is 15 feet from the ground to the top of the tree.
Step-by-step explanation:
Describe the steps you would use to solve the
following inequality
2x - 3
Answer: No answer
Step-by-step explanation:
Not an inequality, inequalities are of the form 2x - 3 > something.
If it's 2x - 3 > 0 for example, then add both sides by 3 to get 2x > 3, then div by 2 to get x > 3/2.
Hope that helped,
-sirswagger21
Simplify [tex]4(y+11)2-3y^2[/tex]
Answer:
[tex]y^2+88y+484[/tex]
Step-by-step explanation:
[tex]4(y+11)^2-3y^2= \\\\4(y^2+22y+121)-3y^2= \\\\4y^2-3y^2+88y+484= \\\\y^2+88y+484[/tex]
Hope this helps!
Simplify.
(8^3)7 = 8n
Answer:
448I think
Step-by-step explanation:
Answer:21
Step-by-step explanation:
Carole's age is five times Joe's age. The sum of their ages is 18. How old are Carole and Joe?
Answer:
Carole is 15
Joe is 3
Step-by-step explanation:
Carole's age is 15
Joes age is 3
3*5=15
15+3=18
Answer:
Carole = 15 Yrs
Joe = 3 Yrs
Step-by-step explanation:
15/5 =3
15+3 =18
Sry for the short explanation. Hope this helps!
If a random sample of size 774 is selected, what is the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3%
Suppose 43% of the population has a retirement account. If a random sample of size 774 is selected, what is the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3%?
Answer:
the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3% is 0.9082
Step-by-step explanation:
Given that:
sample size n = 774
Let P be the population proportion for having a retirement account = 0.43
Also
Let consider [tex]\hat p[/tex] be the sample proportion of having a retirement account.
However; as n is > 30 ; we can say:
[tex]\mathbf{\mu_{\hat p} = 0.43}[/tex] ;
[tex]\mathbf{\sigma_{\hat p^2} = \dfrac{p(1-p)}{n}}[/tex]
⇒ [tex]\mathbf{\sigma_{\hat p^2} = \dfrac{0.43(1-0.43)}{774}}[/tex]
⇒ [tex]\mathbf{\sigma_{\hat p^2} = \dfrac{0.43(0.57)}{774}}[/tex]
So; we need P( the sample proportion will differ from 'p' by less than 3% i.e 0.03)
[tex]=P(| \hat p- p|< 0.03)[/tex]
[tex]=P(| \hat p- \mu _p|< 0.03)[/tex]
[tex]= P ( |\dfrac{\hat P - \mu_p}{\sigma_{\hat p}}|< \dfrac{0.03}{\sqrt{ \dfrac{0.43*0.57}{774} }})[/tex]
[tex]= P(|Z|<1.6859)\ \ \ \ [Z=(\dfrac{\hat P - \mu_{\hat P}}{\sigma_{\hat P}}) \sim N(0,1)][/tex]
[tex]= P(-1.6859 <Z<1.6859) \\ \\ = \Phi(1.6859)- \Phi (-1.6859) \\ \\ = \Phi (1.6859) - (1- \Phi(1.6859) \\ \\ = 2 \Phi (1.6859)-1[/tex]
From Normal Cumulative Distribution Function Table
[tex]= 2*0.9541 -1[/tex]
= 1.9082 - 1
= 0.9082
Thus; the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3% is 0.9082
Based on her weight and pace, Kate burns 586 calories when she runs 5 miles. How many calories will she burn if she runs only 3 miles? How many miles (to the nearest mile) does she need to run each week if she wants to burn one pound (3500 calories) of body fat each week?
Answer:
Dear dandrexbox
Answer to your query is provided below
She will burn 351.6 calories if she run 3 miles.
She needs to run 4 miles (approx) per day for a week to burn one pound calories.
Step-by-step explanation:
Explanation for the same is attached in image
Write the equation 2x - 3y = 6 in slope-intercept form.
Answer:
[tex] y = \frac{ 2}{ 3} x - 2[/tex]
Step-by-step explanation:
[tex]2x - 3y = 6 \\ - 3y = - 2x + 6 \\ \\ y = \frac{ - 2}{ - 3} x + \frac{6}{ - 3} \\ \\ \huge \purple{ \boxed{ y = \frac{ 2}{ 3} x - 2}} \\ this \: is \: in \: the \: slope - intercept \: form.[/tex]
Answer:
y = 2/ 3 x − 2
Step-by-step explanation:
slope intercept is y=mx+b
A box is a cuboid with dimensions 28cm by 15cm by 20cm all measured to the nearest centimetre.
Disc cases are cuboid which measure 1.5 by 14.2 cm by 19.3 cm all measure to the nearest millimetre. Show that 17 disc cases, stacked as shown, will definitely fit the box
Answer:
The 17 disc cases would definitely fit into the box.
Step-by-step explanation:
The given cuboid box has the dimensions 28cm by 15cm by 20cm.
Disc cases are cuboid with dimensions 1.5cm by 14.2cm by 19.3cm.
volume of a cuboid = length × width × height
Volume of the box = 28 × 15 × 20
= 8400 cubic centimeters
Volume of each disc case = 1.5 × 14.2 × 19.3
= 411.09 cubic centimeters
When the 17 disc cases are stacked it would have a volume.
The volume of 17 disc cases = 17 × volume of a case
= 17 × 411.09
= 6988.53 cubic centimeters
Thus comparing the volume for 17 disc cases and that of the cuboid box, the disc cases would definitely fit into the box.
i.e = [tex]\frac{volume of box}{volume of 17 disc cases}[/tex]
= [tex]\frac{8400}{6988.53}[/tex]
= 1.20
Answer:
Step-by-step explanation:
27.5×14.5×19.5 =7775.625 cm³
1.55 x 14.25 x 19.35=427.393125
427.393125 x 17=7265.683
7775.625>7265.683
19.5x27.5x14.5=7775.625
1.45x14.15x19.25=394.961875
394.961875x17=6714.35
7775.63>6714.35
1.55x17=26.35
27.5>26.35
How many days are there in 12 weeks? Use the following information to convert this time to days. 1 week = 7 days
Answer:
84days
Step-by-step explanation:
1 week = 7days =>12 weeks = 12×7 = 84days
Answer:
84 days are in 12 weeks
Step-by-step explanation:
1 week = 7 days
4 weeks = 28 days
So 28 + 28 + 28 = 84 days
Leila runs each lap in 6 minutes. She will run less than 9 laps today. What are the possible numbers of minutes she will run today? Use t for the number of minutes she will run today. Write your answer as an inequality solved for t.
Answer:
I'm not sure if Leila is allowed to run 0 laps.
6 ≤ t ≤ 48
Step-by-step explanation:
To find the number of possible laps, you just find the smallest possible number and the largest.
1 = smallest
8 = largest
But, you have to multiply by 6 to find the time.
6 ≤ t ≤ 48
lucy buys 3 liters of apple juice. How many millilitres of apple juice does she buy?
*please help*
Answer:
3000 milliliters
Step-by-step explanation:
1liter contains 1000militers
3liters contain (3*1000)militers
Answer:
3000 millilitres
Step-by-step explanation:
since 1 litre = 1000 millimetres
3 litres will be equal to 1000 x 3 = 3000 ml
A particular extension cord can support up to 8 amps. Mo has an iron whose label states 1,200 watts and wonders if the iron can be plugged into the extension cord. If watts are converted to amps by dividing by 120, how many amps does the iron use?
Answer:
10 AStep-by-step explanation:
Given data
Current in cord is I = 8 a m p
Power of iron is P = 1200 W
Voltage converted is
V = 120 V
The power can be expressed as
[tex]P=IV=\\I=\frac{P}{V}[/tex]
Substitute the given value in above we get,
I = [tex]\frac{1200}{120}= 10amps[/tex]
Thus, the current use by iron is
10 A
