Answer:
Number of bags that Bonnie can make so that each one has the same number of candies = 48
Number of candies from bag I in each of the treat bag = 5
Number of candies from bag II in each of the treat bag = 13
Number of candies from bag III in each of the treat bag = 7
Step-by-step explanation:
Given: One bag (I) has 240 candies, one bag (II) has 624 candies and one bag (III) has 336 candies
To find: Number of bags that Bonnie can make so that each one has the same number of candies and number of each type of candies in each bag
Solution:
[tex]240=2^4\times 3\times 5\\624=2^4\times3\times13\\336=2^4\times3\times7[/tex]
Highest common factor (H.C.F) = [tex]2^4\times3=48[/tex]
So,
Number of bags that bonnie can make so that each one has the same number of candies = 48
Now,
[tex]\frac{240}{48}=5\\ \frac{240}{48}=13\\\frac{240}{48}=7[/tex]
Number of candies from bag I in each of the treat bag = 5
Number of candies from bag II in each of the treat bag = 13
Number of candies from bag III in each of the treat bag = 7
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.
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
Divide £2.28 btw eve and amelie in the ratio 9:5 give your answer to the nearest penny Eve gets ? And amelie gets ?
Answer:
Eve gets 1.47 and Amelie gets 0.81
Step-by-step explanation:
the ratio is 9 to 5 so we can say 9x + 5x=2.28
14x=2.28
x=0.16
so eve gets 9x = 9(2.28/14) = 1.47
and amelie gets 5x = 5(2.28/14) = 0.81
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
Solve for n.
11(n – 1) + 35 = 3n
n = –6
n = –3
n = 3
n = 6
Answer:
[tex]n = - 3[/tex]
Second answer is correct
Step-by-step explanation:
[tex]11(n - 1) + 35 = 3n \\ 11n - 11 + 35 = 3n \\ 11n - 3n = 11 - 35 \\ 8n = - 24 \\ \frac{8n}{8} = \frac{ - 24}{8} \\ n = - 3[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
The average score Josie had in 6 subjects is 72 and her average score after 2 additional subjects were added is 74.25. If she scored 80 in the 7th subject, what was her score in the 8th subject correct to the nearest whole number?
Answer:82
Step-by-step explanation:
a+b+c+d+e+f/6=72
a+b+c+d+e+f=6*72
a+b+c+d+e+f=432
a+b+c+d+e+f+g+h/8=74.25
a+b+c+d+e+f+g+h=594
g=80
h=?
432+80+h=594
512+h=594
h=82
hope it helps brainleast plz...
I am divisible by 3.
I am an even number.
I am the missing number
in 48/x=8.
Who am I?
Answer:
You are 6
Step-by-step explanation:
8×6=48 and 6/3=2
6 is even and fits in all of these areas.
Hope this helps.
Mark brainliest if correct.
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
Find the area of the smaller sector.
Round to the nearest tenth.
Help needed fast
Answer:
About 22.2 square feet
Step-by-step explanation:
First, you need to find the area of the full circle. The area of a circle is \pi r^2, which in this case is:
[tex]\pi r^2 = \pi \cdot 7.13^2\approx 159.628[/tex]
Now, since the sector is only 50 out of the total 360 degrees in a circle, you need to multiply this value by 50/360, which yields and area of about 22.2 square feet. Hope this helps!
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 store has 80 modems in its inventory, 30 coming from Source A and the remainder from Source B. Of the modems from Source A, 20% are defective. Of the modems from Source B, 8% are defective. Calculate the probability that exactly two out of a sample of five modems selected without replacement from the store’s inventory are defective.
Answer:
0.102
Step-by-step explanation:
The number of defective modems in the inventory is 20% * 30 + 8% * 0.50 =10 (out of 80)
Note that the number of defectives in the inventory is fixed i.e. we are told that there is 1/8 probability that a modem in the inventory is defective, but rather that exactly 1/8 of all modems are defective.
The probability that exactly two modems in a random sample of five are defective is :
(10↓2)(70↓3) / (80↓5) = 0.102
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
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
Translate the phrase into a variable expression. Use the letter d to name the variable. If necessary use the asterisk for multiplication and the slash for division The numbers of dollars Paul owes plus 16..
Answer:
This can be written as d + 16 because plus means addition.
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.
Triangle ABC has been dilated about point A by a scale factor of One-third.
Triangle A B C. Side A C has a length of 39, side A B is 30, side C B is 48. Triangle A prime B prime C prime.
What are the lengths, in units, of the three sides of Triangle A prime B prime C prime?
Answer:
10,16,13
Step-by-step explanation:
got that right
The lengths of the sides of the triangle after the dilation is 13 , 10 and 16 respectively
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the triangle be represented as ABC
Now , the dilated triangle is represented as A'B'C'
The dilation scale factor is d = 1/3
The measure of side AC = 39
The measure of side AB = 30
The measure of side BC = 48
Now , after the dilation of 1/3 , we get
The measure of side A'C' = 39 ( 1/3 ) = 13
The measure of side A'B' = 30 ( 1/3 ) = 10
The measure of side B'C' = 48 ( 1/3 ) = 16
Hence , the dilation triangle is having lengths 13 , 10 and 16
To learn more about dilation click :
https://brainly.com/question/13176891
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A survey asks teachers and students whether they would like the new school
mascot to be a shark or a moose. This table shows the results. Which
statement is true?
A 2-pack of scented candles costs $0.95. What is the unit price, rounded to the nearest cent?i mark the 1st answer brainliest
Step-by-step explanation:
Cost of 2 pack = 0.95
Cost of 1 pack = 0.95 ÷ 2 = 0.475
Unit price = 0.475
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!
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
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
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
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
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 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:
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:
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)])
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!
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
A taxi company manager is trying to decide whether the use of radial tires instead of regular belted tires improves fuel economy. Twelve cars were equipped with radial tires and driven over a prescribed test course. Without changing drivers, the same cars were then equipped with regular belted tires and driven once again over the test course. The gasoline consumption, in kilometers per liter, was recorded as follows:
Car Radial-Tires Belted-Tires
1 4.2 4.1
2 4.7 4.9
3 6.6 6.2
4 7.0 6.9
5 6.7 6.8
6 4.5 4.4
7 5.7 5.7
8 6.0 5.8
9 7.4 6.9
10 4.9 4.7
11 6.1 6.0
12 5.2 4.9
A two-sample t-test was used to compare the mean kilometers per liter for the two types of tires using a .05 level of significance. The resulting p-value was .0152.
State the null and alternate hypotheses, state whether the null hypothesis should be rejected or not rejected and your reason for that conclusion, state the meaning of that conclusion specifically in terms of the problem being studied.
Answer:
Step-by-step explanation:
Corresponding gasoline consumption when radial tires is used and gasoline consumption when regular belted tires is used form matched pairs.
The data for the test are the differences between the gasoline consumption when radial tires is used and gasoline consumption when regular belted tires is used.
μd = the gasoline consumption when radial tires is used minus the gasoline consumption when regular belted tires is used.
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The resulting p-value was .0152.
Since alpha, 0.05 > than the p value, 0.0152, then we would reject the null hypothesis. Therefore, at 5% significance level, we can conclude that the gasoline consumption when regular belted tires is used is higher than the gasoline consumption when radial tires is used.
