Answer:
Yes, her reasoning is correct
Step-by-step explanation:
Given the ratio: 109.2 : 6
Written in fractional form, we have:
[tex]109.2: 6=\dfrac{109.2}{6}[/tex]
Now:
[tex]\dfrac{109.2}{6}=\dfrac{109.2}{6}X1, $ Let 1=\dfrac{10}{10}, \\\\=\dfrac{109.2}{6}X\dfrac{10}{10}\\\\=\dfrac{1092}{60}[/tex]
Therefore, the student's reasoning is correct. In fact, as a check:
[tex]\dfrac{109.2}{6}=18.2\\\\\dfrac{1092}{60}=18.2[/tex]
We would obtain the same result in both cases.
Answer:
yes
Step-by-step explanation:
10,25,35,45... What's the pattern?
Answer:
15
Step-by-step explanation:
The pattern is going by 15 because 10+15=25 and then continue going.
Answer:
15 is the answer
Step-by-step explanation:
Rainwater was collected in water collectors at thirty different sites near an industrial basin and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.9 and 1.5 respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding 0.2 pH units to all of the values and then multiply the result by 1.3. Find the mean and standard deviation of the corrected pH measurements.
Answer:
The mean and standard deviation of the corrected pH measurements are 6.63 and 3.8025 respectively.
Step-by-step explanation:
We can correct the values of the mean and standard deviation using the properties of the mean and the variance.
To the original value X we have to add 0.2 and multiply then by 1.3 to calculate the new and corrected value Y:
[tex]Y=1.3(X+0.2)[/tex]
The mean and standard deviation of the original value X are 4.9 and 1.5 respectively.
Then, we can apply the properties of the mean as:
[tex]E(Y)=E(1.3(X+0.2))=1.3E(X+0.2)=1.3E(X)+1.3*0.2\\\\E(Y)=1.3E(X)+0.26\\\\E(Y)=1.3*4.9+0.26=6.37+0.26=6.63[/tex]
For the standard deviation, we apply the properties of variance:
[tex]V(Y)=V(1.3(X+0.2))\\\\V(Y)=1.3^2\cdot V(X+0.2)\\\\V(Y)=1.69\cdot V(X)\\\\V(Y)=1.69\cdot 1.5^2=1.69\cdot 2.25=3.8025[/tex]
The properties that have been applied are:
[tex]1.\,E(aX)=aE(X)\\\\ 2.\,E(X+b)=E(X)+b\\\\3.\,V(aX)=a^2V(X)\\\\4.\,V(X+b)=V(X)+0[/tex]
On a game show, 14 contestants qualified for the bonus round and 6 contestants did not.
What is the experimental probability that the next contestant will qualify for the bonus round?
Write your answer as a fraction or whole number.
Answer:
The experimental probability that the next contestant will qualify for the bonus round is [tex]\frac{7}{10}[/tex]
Step-by-step explanation:
The experimental probability of an outcome is the number of trials in which the desired outcome happened divided by the total number of trials.
What is the experimental probability that the next contestant will qualify for the bonus round?
14 contestants qualified out of 14+6 = 20 contestants. So
[tex]p = \frac{14}{20} = \frac{7}{10}[/tex]
The experimental probability that the next contestant will qualify for the bonus round is [tex]\frac{7}{10}[/tex]
You look at a caterpillar under a magnifying glass. The image of the caterpillar is three times the caterpillar's actual size and has a width of 4 in. Find the actual dimension of the caterpillar. Select one: a. 12 in. b. 3 in. c. 4/3 in. d. 3/4 in.
Answer: c
Step-by-step explanation: 4/1 x 1/3 = 4/3
Find the point estimate for the true difference between the given population means.
Weights (in Grams) of Soap Bar A: 121, 122, 124, 123, 120, 124, 121, 121, 121, 123, 120
Weights (in Grams) of Soap Bar B: 121, 120, 122, 119, 121, 122, 122, 120, 120, 121, 122, 123, 119
Answer:
0.9 grams
Step-by-step explanation:
The point estimate for the average weight of Soap Bar A is:
[tex]A=\frac{121+122+124+ 123+ 120+ 124+ 121+ 121+ 121+ 123+ 120}{11}\\A=121.82\ grams[/tex]
The point estimate for the average weight of Soap Bar B is:
[tex]B=\frac{121+120+122+ 119+ 121+ 122+ 122+ 120+ 120 +121+ 122+123+119}{13}\\B=120.92\ grams[/tex]
Therefore, the point estimate for the true difference between the given population means is:
[tex]Dif = A-B\\Dif = 121.82-120.92\\Dif=0.9\ grams[/tex]
The point estimate for the difference is 0.9 grams.
The ratio of boys to girls in a club is 4:3. If there are 48 boys, how many members of the club are there?
Answer:
84
Step-by-step explanation:
Basically the ratio was multiplied by 12 to get the number of boys so you do the same to the other one.
Answer:
number of boys+number of girls=48boys+36girls=84members
Step-by-step explanation:
FIRST WE FIND THE NUMBER OF GIRLS BY STATISTICAL METHOD
4:3=48:x
4/3=48/x
By cross multiplication
4×x=48×3
4x=144
Dividing 4 on both sides
4x/4=144/4
x=36=number of girls
Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 50.7 degrees. Low Temperature (circleF) 40 minus 44 45minus49 50 minus 54 55 minus 59 60 minus 64 Frequency 2 7 9 5 1 The mean of the frequency distribution is nothing degrees. (Round to the nearest tenth as needed.)
Answer:
51.2°FStep-by-step explanation:
Find the exact frequency table in the diagram attached. x is the midpoint of the interval f is the frequency. Using the formula below to find the mean;
[tex]\overline x = \frac{\sum fx}{\sum f} \\[/tex]
[tex]\sum fx = (42*2)+(47*7)+(52*9)+(57*5)+(62*1)\\\sum fx = 84+329+468+285+62\\\sum fx = 1,228\\\sum f = 24\\\\\overline x = \frac{1,228}{24} \\\overline x = 51.17^{0} F[/tex]
The mean of the frequency distribution compare to the actual mean of 50.7°F is 51.2°F(to nearest tenth)
Which statement describes the graph of this polynomial function?
f(x) = x5-6x4+9x3
The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.
O The graph touches the x-axis at x = 0 and crosses the x-axis at x = 3.
O The graph crosses the x-axis at x = 0 and touches the x-axis at x = -3.
O The graph touches the x-axis at x = 0 and crosses the x-axis at x = -3.
Answer:
The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.
Step-by-step explanation:
When you graph this equation, you should see the zeros it passes and touches.
Answer:
A. The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.
Step-by-step explanation:
Each of four tables at a party is set bowl with a bowl of grapes each Bowl contains 5/8 of a pound of grapes how many pounds of grapes are there altogether show your work
Answer:
2.5 pounds
Step-by-step explanation:
A graphic designer wants to translate rectangle DEFG using T–1, 2(x, y). The pre-image has coordinates D(–1, 3),
E(4, 3), F(4, 1), and G(–1, 1). What is the image of DEFG?
Answer:
D'(-2, 5), E'(3, 5), F'(3, 3), G'(-2, 3)
Step-by-step explanation:
Adding (-1, 2) to each of the coordinates gives ...
D +(-1, 2) = (-1-1, 3+2) = D'(-2, 5)
E +(-1, 2) = (4-1, 3+2) = E'(3, 5)
F +(-1, 2) = (4-1, 1+2) = F'(3, 3)
G +(-1, 2) = (-1-1, 1+2) = G'(-2, 3)
Answer:
The answer is B.
Step-by-step explanation:
I got it correct on Edge 2020
value of 2 to the 3 power
Answer:
two to the thrid power is 8.
Step-by-step explanation:
2^3= 8
Answer:
I'm not sure what exactly the question is but it should be 8
Step-by-step explanation:
2^3
2×2×2=8
An attendant at a car wash is paid according to the number of cars that pass through. Suppose that following payments are made with the following probabilities: Payment Probability $7 0.18 $9 0.08 $11 0.09 $13 0.16 $15 0.08 $17 0.41 Find the standard deviation of the attendant's earnings.
Answer:
[tex] E(X) = 7*0.18 +9*0.08 +11*0.09 +15*0.08 +17*0.41 =13.22[/tex]
And we can find the second moment with this formula:
[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]
And replacing we got:
[tex] E(X^2) = 7^2*0.18 +9^2*0.08 +11^2*0.09 +15^2*0.08 +17^2*0.41 =189.72[/tex]
And we can find the variance like this:
[tex] Var(X) = E(X^2) -[E(X)]^2= 189.72- (13.22)^2 =14.9516[/tex]
And the deviation would be:
[tex] Sd(X)= \sqrt{14.9516}= 3.867[/tex]
Step-by-step explanation:
For this case we have the following dataset given:
Payment $7 $9 $11 $13 $15 $17
Probability 0.18 0.08 0.09 0.16 0.08 0.41
For this case we can calculate the mean with this formula:
[tex] E(X) = \sum_{i=1}^n X_i P(X_i)[/tex]
And replacing we got:
[tex] E(X) = 7*0.18 +9*0.08 +11*0.09 +15*0.08 +17*0.41 =13.22[/tex]
And we can find the second moment with this formula:
[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]
And replacing we got:
[tex] E(X^2) = 7^2*0.18 +9^2*0.08 +11^2*0.09 +15^2*0.08 +17^2*0.41 =189.72[/tex]
And we can find the variance like this:
[tex] Var(X) = E(X^2) -[E(X)]^2= 189.72- (13.22)^2 =14.9516[/tex]
And the deviation would be:
[tex] Sd(X)= \sqrt{14.9516}= 3.867[/tex]
A recursion formula and the initial term of a sequence are given. Write out the first five terms of the sequence. a Subscript font size decreased by 1 1equals6, a Subscript n plus font size decreased by 1 1equalsminusa Subscript n
Answer:
6, -6, 6, -6 and 6.
Step-by-step explanation:
Given the recursion formula for a sequence
[tex]a_{n+1}=-a_n\\$where a_1=6\\[/tex]
The first five terms of the sequence are:
[tex]\text{First Term, }a_1=6\\$Second Term, a_2=a_{1+1}=-a_1=-6\\$Third term, a_3=a_{2+1}=-a_2=6\\$Fourth term, a_4=a_{3+1}=-a_3=-6\\$Fifth term, a_5=a_{4+1}=-a_4=6[/tex]
Therefore, the first five terms of the sequence:
[tex]a_1,a_2,a_3,a_4,a_5=6, -6, 6, -6$ and 6.[/tex]
Can someone help me figure out the steps to get the answer:)
Answer:
c = ± 8.363277
Step-by-step explanation :
[tex]5.72^{2} = 32.49\\\\6.12^{2} = 37.4544\\3.49 + 37.4544 = 69.9444\\\\c^{2} = \sqrt{69.9444} \\= 8.363277[/tex]
What’s the correct answer for this?
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Tangents that meet at a point are equal in length so DB = CB
Let's form an equation:
10x + 16 = 5x + 20
- 16 from both sides
10x = 5x + 4
- 5x from both sides
5x = 4
/5 on both sides
x = 4/5
Sub this value into the expression for CB
5(4/5) + 20 = 24
Thus, the answer is option D. 24
Have A Nice Day ❤
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Answer:
4TH OPTION
Step-by-step explanation:
IN A CIRCLE , TANGENT DRAWN FROM AN EXTERNAL POINT TO THE CIRCLE ARE EQUAL.
ie BD = BC
ie 10x +16 = 5x+20
10x - 5x = 20 -16
5x = 4
x = 4/5
therfore BC = 5x+20 = 5*4/5 +20
BC= 4+20
BC = 24
HOPE IT HELPS...
The arithmetic sequence a1 is defined by the formula:
a1 = 4
a1=ai-1 +11
Find the sum of the first 650 terms in the sequence.
Answer:
2,322,775
Step-by-step explanation:
Given a1 = 4 and ai =ai-1 +11
when i = 2
a2 = a2-1+11
a2 = a1+11
a2 = 4+11
a2 = 15
when i = 3
a3 = a2+11
a3 = 15+11
a3 = 26
The sequence formed by a1, a2, a3... is am arithmetic sequence as shown;
4, 15, 26...
Sum of nth term of an arithmetic sequence = n/2{2a+(n-1)d}
a is the first term = 4
d is the common difference = 15-4 = 26-15 = 11
n is the number of terms.
Since we are to find the sum of the first 650 terms in the sequence, n = 650
S650 = 650/2{2(4)+(650-1)11}
S650 = 325{8+(649)11}
S650 = 325(8+7,139)
S650 = 325×7147
S650 = 2,322,775
hiii guys i need help with my homewrok [tex]-9\leq 7-8x[/tex]
Answer:
The answer is x ≤ 2.
Step-by-step explanation:
Firstly, you have to move the unrelated term to the other side :
[tex] - 9 \leqslant 7 - 8x[/tex]
[tex] - 9 - 7 \leqslant - 8x[/tex]
[tex] - 16 \leqslant - 8x[/tex]
Next you can solve it :
[tex] - 8x \geqslant - 16[/tex]
[tex]x \leqslant - 16 \div - 8[/tex]
[tex]x \leqslant 2[/tex]
*Remember to change the symbol, when it is dividing by a negative value
Answer the question above?
Answer:
m>n
Step-by-step explanation:
The value of m
The sum of the angles of a triangle are 180
50+30 + m = 180
m = 180-50-30
m = 100
The value of n
The sum of the angles of a triangle are 180
28 + 58+n = 180
n = 180-58-28
n=94
m>n
Question 6
An experiment consists of rolling a single die 12 times and the variablex is the number of times that the outcome is 6. Use binomial distribution to find the probability that the
outcome of 6 occurs exactly 3 times
Answer:
[tex] P(X=3)[/tex]
And using the probability mass function we got:
[tex] P(X=3)= (12C3)(\frac{1}{6})^3 (1-\frac{1}{6})^{12-3}=0.1974[/tex]
Step-by-step explanation:
Let X the random variable of interest "number of times that 6 appears", on this case we now that:
[tex]X \sim Binom(n=12, p=1/6)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X=3)[/tex]
And using the probability mass function we got:
[tex] P(X=3)= (12C3)(\frac{1}{6})^3 (1-\frac{1}{6})^{12-3}=0.1974[/tex]
Please help i do not understand this one!
Answer:
B. [[0,4]
[-6,1]
[3,-4]]
Step-by-step explanation:
If you multiply the matrices, you get the answer.
One number is 1/2 another number. The sum of the two numbers is 33. Find the two numbers.
Answer:
11
Step-by-step explanation:
I looked it up for you so no problem
Answer: 11 and 22
Step-by-step explanation:
We can start by making an equation. Since we know we have two numbers added to make 33. One number can be represented by x and the other is half of this x number so we can write this equation.
33 = 1/2x + x
Now we can combine like terms.
33 = 3/2x
Then either multiply by the reciprocal or divide by 1.5 on both sides.
x = 22
And the other number is half this number so divide by 2.
y = 11
How many 1/2 are there in 6/4
Answer:
3
Step-by-step explanation:
6/4 (divide numerator and denominator each by 2)
= 3/2
= 3 x (1/2)
hence there are 3 halves in 6/4
Answer:
3
Step-by-step explanation:
To find out, we need to divide.
[tex]\frac{6}{4}[/tex] ÷ [tex]\frac{1}{2}[/tex]
When dividing fractions, you multiply the 1st term by the second term's reciprocal.
so
[tex]\frac{6}{4}[/tex] x 2
If you simplify you get [tex]\frac{6}{2}[/tex] or 3.
15 divided by 6 2/3=
Answer:
The answer is D.
Step-by-step explanation:
First, you have to convert the mixed number into improper fraction :
[tex]6 \frac{2}{3} [/tex]
[tex] = \frac{3 \times 6 + 2}{3} [/tex]
[tex] = \frac{20}{3} [/tex]
Next, you can divide it by cutting out the common factor :
[tex]15 \div \frac{20}{3} [/tex]
[tex] = 15 \times \frac{3}{20} [/tex]
[tex] = 3 \times \frac{3}{4} [/tex]
[tex] = \frac{9}{4} [/tex]
[tex] = 2 \frac{1}{4} [/tex]
The value of the expression after divide is,
⇒ 2 1/4
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The expression is,
⇒ 15 divided by 6 2/3
Now,
We can divide as;
⇒ 15 divided by 6 2/3
⇒ 15 ÷ 6 2/3
⇒ 15 ÷ 20/3
⇒ 15 × 3/20
⇒ 45/20
⇒ 9/4
⇒ 2 1/4
Learn more about the divide visit:
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What value of x is in the solution set of 3(x – 4) ≥ 5x + 2? –10 –5 5 10
Answer:I think it -5 wait lemme check answer again
The solution to the inequality will be greater than or equal to –5. Then the correct option is B.
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 inequality is given below.
3(x – 4) ≥ 5x – 2
Simplify the equation, then the solution to inequality will be
3(x – 4) ≥ 5x –2
3x – 12 ≥ 5x –2
5x – 3x ≤ – 12 + 2
2x ≤ – 10
x ≤ –5
The solution to the inequality will be greater than or equal to –5.
Then the correct option is B.
The correct equation is 3(x – 4) ≥ 5x – 2.
More about the inequality link is given below.
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Suppose the high tide in Seattle occurs at 1:00 a.m. and 1:00 p.m. at which time the water is 10 feet above the height of the low tide. Low tides occur 6 hours after high tides. Suppose there are two high tides and two low tides every day and the height of the tide varies sinusoidally.
a) Find a formula for the function y = h(t) that computes the height of the tide above low tide at time t. (In other words, y = 0 corresponds to low tide)
b) What is the tide height at 11:00 am?
Answer:
The low tide, when it is 10 feet below the high tide would be at 7am and 7pm
Step-by-step explanation:
Does anyone know this? I think its B? Am i correct?
Yes, B. Rising action is correct
Which point satisfies both ƒ(x) = 2x and g(x) = 3x?
Answer:
(0,0)
Step-by-step explanation:
If a point satisfies both functions, they must be equal to each other. Thus, we have:
[tex]f(x)=g(x)[/tex]
[tex]2x=3x[/tex]
The only x that satisfies this is 0.
Therefore, the y is also zero.
The point is (0,0).
Alternatively, you can also visualize the graphs. The only point where the graphs will touch is the origin point or (0,0).
A certain bridge arch is in the shape of half an ellipse 106 feet wide and 33.9 feet high. At what horizontal distance from the center of the arch is the height equal to 12.3 feet
Answer:
The horizontal distance from the center is 49.3883 feet
Step-by-step explanation:
The equation of an ellipse is equal to:
[tex]\frac{x^2}{a^{2} } +\frac{y^2}{b^{2} } =1[/tex]
Where a is the half of the wide, b is the high of the ellipse, x is the horizontal distance from the center and y is the height of the ellipse at that distance.
Then, replacing a by 106/2 and b by 33.9, we get:
[tex]\frac{x^2}{53^{2} } +\frac{y^2}{33.9^{2} } =1\\\frac{x^2}{2809} +\frac{y^2}{1149.21} =1[/tex]
Therefore, the horizontal distances from the center of the arch where the height is equal to 12.3 feet is calculated replacing y by 12.3 and solving for x as:
[tex]\frac{x^2}{2809} +\frac{y^2}{1149.21} =1\\\frac{x^2}{2809} +\frac{12.3^2}{1149.21} =1\\\\\frac{x^2}{2809}=1-\frac{12.3^2}{1149.21}\\\\x^{2} =2809(0.8684)\\x=\sqrt{2809(0.8684)}\\x=49.3883[/tex]
So, the horizontal distance from the center is 49.3883 feet
What is the decimal equivalent of 23/9
Answer:
2.555555
Step-by-step explanation: Nine times 2 is 18. When we subtract 18 from 23 we get 5. In the quotient we add a decimal point and add a zero to 5 which is 50. Nine times 5 is 45. When we subtract 45 from 50 we get 5 again and again and again . In decimal form it is 2.5555555.
Answer:
2.55 Hope this helps!
A University of Florida economist conducted a study of Virginia elementary school lunch menus During the state-mandated testing period, school lunches average 863 calories The economist claims that after the testing period ends, the average caloric content of Virginia school lunches drops significantly They collected a random sample of 500 students' school lunches around Virginia
a). What null and alternative hypotheses should you test?
b). Set up the rejection region for this study using alpha = 0.05 Interpret alpha = 0.05 in the words of the problem
c). Suppose the sample data yielded the test statistic z = -2.17 What conclusion can you draw for the test?
d). Calculate the observed p-value for the test statistic z = -2.17 Interpret the p-value and draw the conclusion based on it
Answer:
a) Null hypothesis: [tex] \mu \geq 863[/tex]
Alternative hypothesis: [tex] \mu >863[/tex]
b) For this case using the significance level of [tex]\alpha=0.05[/tex] we can use the normal standard distirbution in order to find a quantile who accumulates 0.05 of the area in the left and we got:
[tex] z_{\alpha}=-1.64[/tex]
And the rejection zone would be:
[tex] z<-1.64[/tex]
c) For this case since the statistic calculated is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance
d) [tex] p_v = P(z<-2.17) =0.015[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at the significance level provided
Step-by-step explanation:
Part a
We want to test for this case if the true mean is significantly less than 863 calories so then the system of hypothesis are:
Null hypothesis: [tex] \mu \geq 863[/tex]
Alternative hypothesis: [tex] \mu >863[/tex]
Part b
For this case using the significance level of [tex]\alpha=0.05[/tex] we can use the normal standard distirbution in order to find a quantile who accumulates 0.05 of the area in the left and we got:
[tex] z_{\alpha}=-1.64[/tex]
And the rejection zone would be:
[tex] z<-1.64[/tex]
Part c
For this case since the statistic calculated is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance
Part d
For this case the p value would be given by:
[tex] p_v = P(z<-2.17) =0.015[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at the significance level provided
