Answer:
Let June's sweets be 5x.
Then Gavyn's sweets will be 5x.
And Alex's sweets will be 3x.
5x = 3x + 22
2x = 22
x = 11
So June has 5 x 11 = 55 sweets
Gavyn has 5 x 11 = 55 sweets
And Alex have 3 x 11 = 33 sweets
Total
= 55 + 55 + 33
= 143 sweets
Mai drives a truck for a soft drink company. Her truck is filled with 15-ounce cans and 70-ounce bottles. Let c be the number of 15-ounce cans the
truck is carrying, and let b be the number of 70-ounce bottles.
The truck must be carrying less than 4000 pounds (64,000 ounces). Using the values and variables given, write an inequality describing this.
Answer:
15c + 70b < 64,000
Step-by-step explanation:
15c will represent the amount of ounces in the truck from the 15 ounce cans.
70b will represent the amount of ounces in the truck from the 70 ounce bottles.
These need to be added together in the inequality to represent the total weight in the truck.
Then, a less than inequality sign needs to be used, since the truck has to be carrying less than 64,000 ounces.
Put this all together:
15c + 70b < 64,000
So, the inequality is 15c + 70b < 64,000
Draw a triangle ABC, where AB = 8 cm , BC = 6 cm and angle B=70^ and locate its circumcentre and draw the circumcircle.
Step-by-step explanation:
ΔABC, where AB = 8 cm, BC = 6 cm, B = 70° Construction: (i) Draw the ∆ABC with the given measurements. (ii) Construct the perpendicular bisector at any two sides (AB and BC) and let them meet at S which is the circumcircle. (iii) S as centre and SA = SB = SC as radius, draw the circumcircle to pass through A, B, and C. Circum radius = 4.3cm .draw-triangle-abc-where-cm-bc-and-70-and-locate-its-circumcentre-and-draw-the-circumcircle
The fracture strength of a certain type of manufactured glass is normally distributed with a mean of 509 MPa with a standard deviation of 17 MPa. (a) What is the probability that a randomly chosen sample of glass will break at less than 509 MPa
Answer:
0.5 = 50% probability that a randomly chosen sample of glass will break at less than 509 MPa
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 509 MPa with a standard deviation of 17 MPa.
This means that [tex]\mu = 509, \sigma = 17[/tex]
What is the probability that a randomly chosen sample of glass will break at less than 509 MPa?
This is the p-value of Z when X = 509. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{509 - 509}{17}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a p-value of 0.5
0.5 = 50% probability that a randomly chosen sample of glass will break at less than 509 MPa
Solve the system, or show that it has no solution. (If there is no solution, enter NO SOLUTION. If there are an infinite number of solutions, enter the general solution in terms of x, where x is any real number.)
20x − 80y = 100
−14x + 56y = −70
(x, y) =
Answer:
The system has an infinite set of solutions [tex](x,y) = (x, \frac{x-5}{4})[/tex]
Step-by-step explanation:
From the first equation:
[tex]20x - 80y = 100[/tex]
[tex]20x = 100 + 80y[/tex]
[tex]x = \frac{100 + 80y}{20}[/tex]
[tex]x = 5 + 4y[/tex]
Replacing on the second equation:
[tex]-14x + 56y = -70[/tex]
[tex]-14(5 + 4y) + 56y = -70[/tex]
[tex]-70 - 56y + 56y = -70[/tex]
[tex]0 = 0[/tex]
This means that the system has an infinite number of solutions, considering:
[tex]x = 5 + 4y[/tex]
[tex]4y = x - 5[/tex]
[tex]y = \frac{x - 5}{4}[/tex]
The system has an infinite set of solutions [tex](x,y) = (x, \frac{x-5}{4})[/tex]
Consider the set S of primes less than 15. List the set S . (Input this as a list with no spaces, use commas.) How many subsets does the set have
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Answer:
S = {2, 3, 5, 7, 11, 13}
2^6 = 64 subsets
Step-by-step explanation:
The list of primes less than 15 is ...
S = {2, 3, 5, 7, 11, 13}
__
A set with n unique elements has 2^n unique subsets, including the empty set and the full set. This set of 6 elements has 2^6 = 64 subsets.
NEED HELP
The average amount of money spent for lunch per person in the college cafeteria is $6.75 and the standard deviation is $2.28. Suppose that 18 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.
C. For a single randomly selected lunch patron, find the probability that this
patron's lunch cost is between $7.0039 and $7.8026.
D. For the group of 18 patrons, find the probability that the average lunch cost is between $7.0039 and $7.8026.
Answer:
C.[tex]P(7.0039<x<7.8026)=0.1334[/tex]
D.[tex]P(7.0039<\bar{x}<7.8026)\approx 0.2942[/tex]
Step-by-step explanation:
We are given that
n=18
Mean, [tex]\mu=6.75[/tex]
Standard deviation, [tex]\sigma=2.28[/tex]
c.
[tex]P(7.0039<x<7.8026)=P(\frac{7.0039-6.75}{2.28}<\frac{x-\mu}{\sigma}<\frac{7.8026-6.75}{2.28})[/tex]
[tex]P(7.0039<x<7.8026)=P(0.11<Z<0.46)[/tex]
[tex]P(a<z<b)=P(z<b)-P(z<a)[/tex]
Using the formula
[tex]P(7.0039<x<7.8026)=P(Z<0.46)-P(Z<0.11)[/tex]
[tex]P(7.0039<x<7.8026)=0.67724-0.54380[/tex]
[tex]P(7.0039<x<7.8026)=0.1334[/tex]
D.[tex]P(7.0039<\bar{x}<7.8026)=P(\frac{7.0039-6.75}{2.28/\sqrt{18}}<\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}})<\frac{7.8026-6.75}{2.28/\sqrt{18}})[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=P(0.47<Z<1.96)[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=P(Z<1.96)-P(Z<0.47)[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=0.97500-0.68082[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=0.29418\approx 0.2942[/tex]
Suppose a large shipment of televisions contained 9% defectives. If a sample of size 393 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 3%
Answer:
0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%
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 normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose a large shipment of televisions contained 9% defectives
This means that [tex]p = 0.09[/tex]
Sample of size 393
This means that [tex]n = 393[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.09[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{393}} = 0.0144[/tex]
What is the probability that the sample proportion will differ from the population proportion by less than 3%?
Proportion between 0.09 - 0.03 = 0.06 and 0.09 + 0.03 = 0.12, which is the p-value of Z when X = 0.12 subtracted by the p-value of Z when X = 0.06.
X = 0.12
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.12 - 0.09}{0.0144}[/tex]
[tex]Z = 2.08[/tex]
[tex]Z = 2.08[/tex] has a p-value of 0.9812
X = 0.06
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.09}{0.0144}[/tex]
[tex]Z = -2.08[/tex]
[tex]Z = -2.08[/tex] has a p-value of 0.0188
0.9812 - 0.0188 = 0.9624
0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%
Please help me quick I’ll give brainliest
what graph shows the solution to the equation below log3(x+2)=1
Answer:
The solution to the equation log3(x+2)=1 is given by x=1
Step-by-step explanation:
We are given that
[tex]log_3(x+2)=1[/tex]
We have to find the graph which shows the solution to the equation log3(x+2)=1.
[tex]log_3(x+2)=1[/tex]
[tex]x+2=3^1[/tex]
Using the formula
[tex]lnx=y\implies x=e^y[/tex]
[tex]x+2=3[/tex]
[tex]x=3-2[/tex]
[tex]x=1[/tex]
The weights of certain machine components are normally distributed with a mean of 5.19 ounces and a standard deviation of 0.05 ounces. Find the two weights that separate the top 8% and the bottom 8%. These weights could serve as limits used to identify which components should be rejected
Answer:
The weight that separate the top 8% by 5.2605 and the weight that separate bottom 8% by 5.1195.
Step-by-step explanation:
We are given that
Mean,[tex]\mu=5.19[/tex]
Standard deviation,[tex]\sigma=0.05[/tex]
We have to find the two weights that separate the top 8% and the bottom 8%.
Let x1 and x2 the two weights that separate the top 8% and the bottom 8%.
Z-value for p-value =0.08 =[tex]-1.41[/tex]
For 8% bottom
[tex]Z=\frac{x_1-\mu}{\sigma}=-1.41[/tex]
[tex]\frac{x_1-5.19}{0.05}=-1.41[/tex]
[tex]x_1-5.19=-1.41\times 0.05[/tex]
[tex]x_1=-1.41\times 0.05+5.19[/tex]
[tex]x_1=5.1195[/tex]
For 8% top
p-Value=1-0.08=0.92
Z- value=1.41
Now,
[tex]\frac{x_2-5.19}{0.05}=1.41[/tex]
[tex]x_2-5.19=1.41\times 0.05[/tex]
[tex]x_2=1.41\times 0.05+5.19[/tex]
[tex]x_2=5.2605[/tex]
(x1,x2)=(5.1195,5.2605)
What is graph for the equation y=-4x+1
Answer: The line starts at 1 positive, then from there go -4 (so go to the left) then 1 down from that point.
Step-by-step explanation: the problem is supposed to have been Y= -4/1 +1
Which function is the result of translating f(x)=x^2+14 to the right 5 units and down 6 units
Which expression can be used to determine 50% of 42?
42-2 ,42÷2,42÷10,42-10
Answer:
42÷2
Step-by-step explanation:
The awnser for this question
a student takes two subjects A and B. Know that the probability of passing subjects A and B is 0.8 and 0.7 respectively. If you have passed subject A, the probability of passing subject B is 0.8. Find the probability that the student passes both subjects? Find the probability that the student passes at least one of the two subjects
Answer:
0.64 = 64% probability that the student passes both subjects.
0.86 = 86% probability that the student passes at least one of the two subjects
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Passing subject A
Event B: Passing subject B
The probability of passing subject A is 0.8.
This means that [tex]P(A) = 0.8[/tex]
If you have passed subject A, the probability of passing subject B is 0.8.
This means that [tex]P(B|A) = 0.8[/tex]
Find the probability that the student passes both subjects?
This is [tex]P(A \cap B)[/tex]. So
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(B|A)P(A) = 0.8*0.8 = 0.64[/tex]
0.64 = 64% probability that the student passes both subjects.
Find the probability that the student passes at least one of the two subjects
This is:
[tex]p = P(A) + P(B) - P(A \cap B)[/tex]
Considering [tex]P(B) = 0.7[/tex], we have that:
[tex]p = P(A) + P(B) - P(A \cap B) = 0.8 + 0.7 - 0.64 = 0.86[/tex]
0.86 = 86% probability that the student passes at least one of the two subjects
Classify the following polynomials. Combine any
like terms first.
x^2+3x + 2x - 2x^2
X^3+ 4x - 4x - 4x^2
X^3+2x - X^3- 2x^2+ 3
First simplify all polynomials and rewrite them in descending exponent order.
1. [tex]-x^2+2x[/tex]
2. [tex]x^3-4x^2[/tex]
3. [tex]-2x^2+2x+3[/tex]
Now observe the terms with highest exponents in each expression, in particularly focus on their exponent value,
[tex]-x^2[/tex] with value of 2
[tex]x^3[/tex] with value of 3
[tex]-2x^2[/tex] with value of 2
The value is also known as order of polynomial and it is a way to classify polynomials.
Every order creates a family of polynomials determined by the order (which is always greater than -1)
A polynomial such as (1) and (3) have an orders of 2, which is often called quadratic order and thus the polynomials (1), (3) are classified in the same family of quadratic polynomials, these are polynomials with order of 2.
Polynomial (2) however has an order of 3, which is called cubic order. This polynomial (2) is classified in the family of cubic polynomials.
There are of course many other families, in fact, infinitely many of them because you have order 0, 1, 2, 3, and so on there are precisely [tex]\aleph_0+1[/tex] read as "aleph 0 + 1" (the number of natural numbers + 1 (because 0 is not a natural number)) of polynomial families.
The first few have these fancy names, for example:
order 0 => constant polynomial
order 1 => linear polynomial
order 2 => quadratic polynomial
order 3 => cubic polynomial
order 4 => quartic polynomial
and so on.
Hope this helps!
The speed (S) an object falls varies directly with time. If the speed is 49.0m/s after 5 seconds, then what is the speed after 3 seconds
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Answer:
29.4 m/s
Step-by-step explanation:
Speed is proportional to time, so we have ...
speed / time = s/3 = 49/5
s = 3/5(49) = 29.4
The speed of the object is 29.4 m/s after 3 seconds.
.What is the value of x if 2(x+1) = 16 ?
2(x +1) = 16
Use the distributive property ( multiply 2 by each term inside the parenthesis).
2x + 2 = 16
Subtract 2 from both sides:
2x = 14
Divide both sides by 2:
x = 7
Answer:
7
Step-by-step explanation:
2x+2=16
2x=16-2
x=16-2/2
x=14/2=7
Which point represents the unit rate?
A
B
C
D
Answer:
Point C represents the unit rate
Step-by-step explanation:
Write an algebraic expression for the situation. 28 divided by a number n An algebraic expression for the situation is
Answer:
[tex]\frac{28}{n}[/tex]
Step-by-step explanation:
Find the area of the shaded region in terms of .
Please help :)
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Answer:
50π cm²
Step-by-step explanation:
The radius of the larger circle is 10 cm, so its area is ...
A = πr² = π(10 cm)² = 100π cm²
The area of each smaller circle is ...
A = π(5 cm)² = 25π cm²
Then the shaded area is ...
shaded = large circle - 2 × small circle
shaded = 100π cm² - 2(25π cm²) = 50π cm²
Can you help me answer this question? Screenshot is added.
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Answer:
(c)
Step-by-step explanation:
[tex]\displaystyle\sqrt[3]{xy^5}\sqrt[3]{x^7y^{17}}=\sqrt[3]{x^{1+7}y^{5+17}}=\sqrt[3]{x^6x^2y^{21}y}=\sqrt[3]{x^6y^{21}}\sqrt[3]{x^2y}\\\\=\boxed{x^2y^7\sqrt[3]{x^2y}}[/tex]
A display case of toy rings are marked 5 for $1. If Zach wants to buy 50 toy rings, how much will Zach spend (not including tax)
Answer:
$10
Step-by-step explanation:
5 toys = $1
Zach wants 50 of these
50 ÷ 5 = 10
10 x 1 = 10
= $10
Answer:
10 dollars
Step-by-step explanation:
We can use a ratio to solve
5 rings 50 rings
---------- = --------------
1 dollar x dollars
Using cross products
5*x = 1 * 50
5x = 50
Divide by 5
5x/5 = 50/5
x = 10
You are planning to buy a house for $800,000. City bank offers a 30 year loan at 4.9 % apr ( Annual percentage interest rate) if you put 20 % down. Calculate your expected monthly payment.
Answer:
3396.65
Step-by-step explanation:
Let's start by cacluating the amount the bank is loaning us
800000*.8=640000
Let's now calculate the effective rate: .049/12= .004083333333
let x= payment
[tex]640000=x\frac{1-(1+.004083333333)^{-30*12}}{.004083333333}\\x=3396.651012[/tex]
14. A professor records the number of class days (x) each student misses over the course of a semester and uses a frequency distribution to display the data. What is the probability a student missed exactly 1 day
Question is incomplete, however here's an explanation to solve questions such as this
Answer and explanation:
Probability= number of favorable outcomes/total number of outcomes
The frequency distribution recorded by the professor would show number of times(frequency) each student missed a class day.
We are required to fund the probability that a student would miss class
Probability = number of times the student missed class/ total number of classes missed by all students
Example, if student missed class 20 times in a semester and all students in total missed class 200 times
Probability that the student would miss class=20/200= 1/10
Find the number of integers n that satisfy n^2 < 100.
Answer:
n=-9,-8,-7
Step-by-step explanation:
n<100
but that is the positive square root
\(-10 n is between the negative and positive square root of 100
thus, n=-9,-8,-7
The solution of the inequality n² < 100 will be less than 10.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The inequality is given below.
n² < 100
Simplify the equation, then we have
n² < 100
n² < 10²
n < 10
The solution of the inequality n² < 100 will be less than 10.
More about the inequality link is given below.
https://brainly.com/question/19491153
#SPJ2
Order these numbers from least to greatest.
5.772 , 11/2, 5 6/11, 5.77
Answer:
6/11, 11/2, 5.77, 5.772
Step-by-step explanation:
what is the sum of a 7 term geometric series if the first term is 6 the last term is -24576 and the common ratio is -4
Answer:
Sum = 19,662
Step-by-step explanation:
Given that this is a finite geometric series (meaning it stops at a specific term or in this case -24,576), we can use this formula:
[tex]\frac{a(1-r^n)}{1-r}[/tex], where a is the first term, r is the common ratio, and n is the number of terms.
Substituting for everything and simplifying gives us:
[tex]\frac{6(1-(-4)^7)}{1-(-4)} \\\\\frac{6(16385}{5}\\ \\\frac{98310}{5}\\ \\19662[/tex]
Help ask anyone have any more answers for the eye level program
Answer:
1) -[tex]\sqrt{32}[/tex]
2) -[tex]\sqrt{108}[/tex]
3) -[tex]\sqrt{80}[/tex]
4) -[tex]\sqrt{112}[/tex]
5) -[tex]\sqrt{40}[/tex]
6) -[tex]\sqrt{99}[/tex]
7) -[tex]\sqrt{50}[/tex]
8) -[tex]\sqrt{150}[/tex]
Step-by-step explanation:
please mark this answer as brainlist
The number of measles cases increased 26.3% to 321 cases this year. What was the number of cases prior to the increase? Express your answer rounded correctly to the nearest whole number.
Answer:
The right answer is "[tex]x\simeq 254[/tex]".
Step-by-step explanation:
Let the number of earlier case will be "x".
Now,
⇒ [tex]x+x\times \frac{26.3}{100}=321[/tex]
or,
⇒ [tex]x+x\times 0.263=321[/tex]
By taking "x" common, we get
⇒ [tex]x(1+0.263)=321[/tex]
⇒ [tex]x=\frac{321}{1.263}[/tex]
⇒ [tex]=254.15[/tex]
or,
⇒ [tex]x\simeq 254[/tex]
