Answer:
x=0.5355 or x=-6.5355
First step is to: Isolate the constant term by adding 7 to both sides
Step-by-step explanation:
We want to solve this equation: [tex]2x^2 + 12x - 7 = 0[/tex]
On observation, the trinomial is not factorizable so we use the Completing the square method.
Step 1: Isolate the constant term by adding 7 to both sides
[tex]2x^2 + 12x - 7+7 = 0+7\\2x^2 + 12x=7[/tex]
Step 2: Divide the equation all through by the coefficient of [tex]x^2[/tex] which is 2.
[tex]x^2 + 6x=\frac{7}{2}[/tex]
Step 3: Divide the coefficient of x by 2, square it and add it to both sides.
Coefficient of x=6
Divided by 2=3
Square of 3=[tex]3^2[/tex]
Therefore, we have:
[tex]x^2 + 6x+3^2=\frac{7}{2}+3^2[/tex]
Step 4: Write the Left Hand side in the form [tex](x+k)^2[/tex]
[tex](x+3)^2=\frac{7}{2}+3^2\\(x+3)^2=12.5\\[/tex]
Step 5: Take the square root of both sides and solve for x
[tex]x+3=\pm\sqrt{12.5}\\x=-3\pm \sqrt{12.5}\\x=-3+ \sqrt{12.5}, $ or $x= -3- \sqrt{12.5}\\$x=0.5355 or x=-6.5355[/tex]
Answer:
Step-by-step explanation:
Step 1: Isolate the constant term by adding 7 to both sides of the equation.
Step 2: Factor 2 from the binomial.
Step 3: 9
Step 3 b: 18
Step4: write the trinomial as the square root of a binomial.
Step 5: divide both sides of the equation by 2 Step
6: Apply the square root property of equality Step
7: subtract 3 from both sides of the equation.
Suppose a certain item used to sell for 30 cents per pound, and you see that it’s been marked up to 45 cents per pound. What is the percent increase?
Answer:
50%
Step-by-step explanation:
45 cents is 15 cents more than 30 cents. The increase in cents is 15.
15 is half of 30. Half is also 0.5, 1/2, or 50%. The increase is 50%.
You can also answer this using the percent change formula.
percent change = (new number - old number)/(old number) * 100%
percent change = (45 - 30)/30 * 100%
percent change = 15/30 * 100%
percent change = 0.5 * 100%
percent change = 50%
If the result is positive, it is a percent increase.
If the result is negative, it is a percent decrease.
I need this asap
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle:
A(2,-3) B(4, -3) C(4, 5) D(2,5)
What is the perimeter of the rectangle ABCD?
Answer:
20
Step-by-step explanation:
The rectangle is 2 x 8.
2 + 2 + 8 + 8
What are the factors of the expression below 9x^2+6x+1?
[tex]answer = (3x + 1)\\ solution \\ {9x}^{2} + 6x + 1 \\ = {9x}^{2} + (3 + 3)x + 1 \\ = {9x}^{2} + 3x + 3x + 1 \\ = 3x(3x + 1) + 1(3x + 1) \\ = (3x + 1)(3x + 1) \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
1, 2, 5, 10, 17, 26, 37, whats next
Answer:
50, 65, 82, 101,122,145,170.
Step-by-step explanation:
hope this helps
(Add two to an odd number and continue doing so)
example: 1+1 =2, 2+3 = 5, 5+5 = 10, 10+7 = 17, and so on so forth.
00:00
Gavin counted the number of days until the end of school.
If he counted the days in groups of 7, which list shows the numbers Gavin could have
named?
O
A. 7, 15, 22, 30
B. 7, 14, 21, 30
C. 7, 14, 21, 28
D. 14, 21, 32, 38
Answer:
C. 7, 14, 21, 28
Step-by-step explanation:
Since you know your times tables, you know that multiples of 7 are ...
7, 14, 21, 28
Is 49 + –56 positive or negative?
Answer:
-7. negative
Step-by-step explanation:
49 + -56
49 - 56
-7
Imagine that you are conducting a one-variable chi-square test to investigate the hypothesis that there are equal numbers of cat lovers and dog lovers in the office at work. Having conducted a survey, you found 150 preferred dogs and 120 preferred cats. What would the expected frequencies be in each cell? 135 150 and 120 270 More information is needed to calculate the expected frequencies.
Answer:
135
Step-by-step explanation:
Based on the following information:
- There are 150 dog lovers
- There are 120 cat lovers
So:
The null hypothesis:
H, there are an equal number of dog lovers and cat lovers, so the expected frequency in each cell will be the same and that is:
f = (150 + 120) / 2
f = 270/2 = 135
then the first option of 135 is correct
The sets F and H are given below.
F={c,f,g}
H= {d,e,h)
Find the union of F and H.
Find the intersection of F and H.
Answer:
F ∪ H = {c, d, e, f, g, h}
F ∩ H = { }
Step-by-step explanation:
The union is the list of elements that are in either of the two sets.
F ∪ H = {c, d, e, f, g, h}
The intersection is the list of only those elements that appear in both sets. (There are none.)
F ∩ H = { } . . . . the empty set
Do people walk faster in an airport when they are departing(getting on a plane) or after they have arrived (getting off aplane)? An interested passenger watched a random sample of people departing and a random sample of people arriving and measured the walking speed (in feet per minute) of each. A hypothesis test is to be performed to determine if the mean walking speed is different between departing and arriving passengers at an airport. One of the conditions that must be satisfied for conclusions from atwo-sample t-test to be valid is that the samples are representative of their respective populations. Is the condition satisfied in this problem?
A. The samples will be representative of their respective populations only if both sample sizes are at least 50% of the population sizes.
B. Because the people observed in the study were randomlyselected, the passengers in each sample should be representative of all departing and arriving passengers at the airport where the samples were taken.
C. The departing and arriving passengers in the samples will be representative of all departing and arriving passengers at the airport where the samples were taken as long as walking speeds in both populations follow a normal distribution.
D. As long as each sample size is at least 30, the samples will be representative of their respective populations.
Answer:
B
Step-by-step explanation:
The sample must be represenatative of whole population. Random selection ensures this.
a trapazoid is a quadrilateral with one or more pairs of paralllel sides true or false
yes the answer is( true).
Answer:
The answer is (True)
Step-by-step explanation:
What is the value of the expression?
458+56−134
Answer:
380
Step-by-step explanation:
Order of operations!
(458+56)-134
(514)-134
514-134
380
done!
Answer:
3.8%
Step-by-step explanation:
After evaluating the expression you get 380. You take 380, and turn it into a percentage, move the decimal to the left twice. Giving you 3.8%
Factor the trinomial completely
8a^2+65ab+8b^2
The radius of a 10” pizza is 5”. Using A= pi2, what is the area of the 10” pizza? (Round to the nearest tenth)
How many times larger is the 15” than 10” pizza?
Is this surprising? Why or why not?
If you doubled the diameter of a circle, how many times larger would it’s area become?
Answer:
846^% and then to rond it is 850^%
Step-by-step explanation:
e radius of a 10” pizza is 5”. Using A= pi2, what is the area of the 10” pizza? (Round to the nearest tenth)
The volume of gas V held at a constant temperature in a closed container varies inversely with its pressure P.If the volume of gas is 400 cubic centimeters (cc) . When The pressure is 300 millimeters of mercury ( mm Hg) , find the volume when the pressure is 500 mm Hg .
When the pressure is 500 mm Hg, the volume is
Answer:
240cc
Explanation:
From the expression of the relationship between pressure and volume, we can state mathematical that for two successive volume V1 and V2 and Pressure P1 and P2 we have:
P1V1 = P2V2
V2 = P1V1 / P2
=400×300/500= 240cc
Charlie wants to order lunch for his friends hell order 6 sandwiches and a $2 kids meal for his little brother Charlie has $32 how much can he spend on each sandwich if they are all the same price
Answer:
Charlie spent 5$ per sandwich
Step-by-step explanation:
He ordered 6 sandwiches
6x5 =30
He spent 2$ on kids meal
30+2 = 32$
Hope this helped, if you want please mark branliest it would be appreciated
Answer:
5
Step-by-step explanation:
remove the kids meal first
32-2=30
now, divided 30 dollars by the 6 sandwiches
30÷6 = 5
each sandwhich is 6 dollars
The prior probabilities for events A1 and A2 are P(A1) = 0.20 and P(A2) = 0.50. It is also known that P(A1 ∩ A2) = 0. Suppose P(B | A1) = 0.20 and P(B | A2) = 0.05. If needed, round your answers to three decimal digits. (a) Are A1 and A2 mutually exclusive?
The inclusion-exclusion principle says
P(A1 ∩ A2) = P(A1) + P(A2) - P(A1 ∪ A2)
We know the probability of intersection is 0, so
P(A1) + P(A2) = P(A1 ∪ A2)
which means A1 and A2 are indeed mutually exclusive.
In tests of a computer component, it is found that the mean time between failures is 937 hours. A modification is made which is supposed to increase reliability by increasing the time between failures. Tests on a sample of 36 modified components produce a mean time between failures of 960 hours, with a standard deviation of 52 hours. Using a significance level of .01, test the claim that, for modified components, the mean time between failures is greater than 937 hours. Find the appropriate p-value.
Answer:
Null hypothesis is [tex]\mathbf {H_o: \mu > 937}[/tex]
Alternative hypothesis is [tex]\mathbf {H_a: \mu < 937}[/tex]
Test Statistics z = 2.65
CONCLUSION:
Since test statistics is greater than critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.
P- value = 0.004025
Step-by-step explanation:
Given that:
Mean [tex]\overline x[/tex] = 960 hours
Sample size n = 36
Mean population [tex]\mu =[/tex] 937
Standard deviation [tex]\sigma[/tex] = 52
Given that the mean time between failures is 937 hours. The objective is to determine if the mean time between failures is greater than 937 hours
Null hypothesis is [tex]\mathbf {H_o: \mu > 937}[/tex]
Alternative hypothesis is [tex]\mathbf {H_a: \mu < 937}[/tex]
Degree of freedom = n-1
Degree of freedom = 36-1
Degree of freedom = 35
The level of significance ∝ = 0.01
SInce the degree of freedom is 35 and the level of significance ∝ = 0.01;
from t-table t(0.99,35), the critical value = 2.438
The test statistics is :
[tex]Z = \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \dfrac{960-937 }{\dfrac{52}{\sqrt{36}}}[/tex]
[tex]Z = \dfrac{23}{8.66}[/tex]
Z = 2.65
The decision rule is to reject null hypothesis if test statistics is greater than critical value.
CONCLUSION:
Since test statistics is greater than critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.
The P-value can be calculated as follows:
find P(z < - 2.65) from normal distribution tables
= 1 - P (z ≤ 2.65)
= 1 - 0.995975 (using the Excel Function: =NORMDIST(z))
= 0.004025
Solve for kkk.
\dfrac{k}{4} = \dfrac{3}{8}
4
k
=
8
3
Answer:
[tex]k=\frac{3}{2}[/tex]
Step-by-step explanation:
Given:
[tex]\frac{k}{4}=\frac{3}{8}[/tex]
To find: value of [tex]k[/tex]
Solution:
Cross-multiplying is a method in which the numerator of each (or one) side is multiplied by the denominator of the other side.
[tex]\frac{k}{4}=\frac{3}{8}[/tex]
On cross-multiplication, the equation becomes [tex]k\times 8=4\times 3[/tex]
[tex]8k=12[/tex]
Divides both sides by 8
[tex]\frac{8k}{8}=\frac{12}{8}\\k=\frac{12}{8}=\frac{3}{2}[/tex]
Quarters are currently minted with weights normally distributed and having a standard deviation of 0.065. New equipment is being tested in an attempt to improve quality by reducing variation. A simple random sample of 25 quarters is obtained from those manufactured with the new equipment, and this sample has a standard deviation of 0.047 . Use a 0.05 significance level to test the claim that quarters manufactured with the new equipment have weights with a standard deviation less than 0.065. Does the new equipment appear to be effective in reducing the variation of weights?
Answer:
Yes, the new equipment appear to be effective in reducing the variation of weights.
Step-by-step explanation:
We are given that Quarters are currently minted with weights normally distributed and having a standard deviation of 0.065.
A simple random sample of 25 quarters is obtained from those manufactured with the new equipment, and this sample has a standard deviation of 0.047.
Let [tex]\sigma[/tex] = standard deviation of weights of new equipment.
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\sigma \geq[/tex] 0.065 {means that the new equipment have weights with a standard deviation more than or equal to 0.065}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\sigma[/tex] < 0.065 {means that the new equipment have weights with a standard deviation less than 0.065}
The test statistics that would be used here One-sample chi-square test statistics;
T.S. = [tex]\frac{(n-1)s^{2} }{\sigma^{2} }[/tex] ~ [tex]\chi^{2}__n_-_1[/tex]
where, s = sample standard deviation = 0.047
n = sample of quarters = 25
So, the test statistics = [tex]\frac{(25-1)\times 0.047^{2} }{0.065^{2} }[/tex] ~ [tex]\chi^{2}__2_4[/tex]
= 12.55
The value of chi-square test statistics is 12.55.
Now, at 0.05 significance level the chi-square table gives critical value of 13.85 at 24 degree of freedom for left-tailed test.
Since our test statistic is less than the critical value of chi-square as 12.55 < 13.85, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the new equipment have weights with a standard deviation less than 0.065.
A tour operator has a bus that can accommodate 20 tourists. The operator knows that tourists may not show up, so he sells 21 tickets. The probability that an individual tourist will not show up is 0.02, independent of all other tourists. Each ticket costs 50, and is non-refundable if a tourist fails to show up. If a tourist shows up and a seat is not available, the tour operator has to pay 100 (ticket cost + 50 penalty) to the tourist. What is the expected revenue of the tour operator?
Answer:
The expected revenue is $984.6.
Step-by-step explanation:
The tourist operator sells 21 non-refundable tickets, as the tourist may not show up.
The tourist have a probability of 0.02 of not showing up, independent of each other.
The income is the selling of the 21 tickets at $50 each.
[tex]I=21*50=1,050[/tex]
The only cost considered in this problem is the refund if a tourist show up and a seat is not available.
This only happens when the 21 tourists show up. If each tourist has a probability of 0.02 of not showing up, they have a probability of 0.98 of showing up.
For the event that the 21 tourists show up, we have the probability:
[tex]P=0.98^{21}\approx0.654[/tex]
For each of this event, the tour operator has to pay $100, so the expected revenue of the tour operator is:
[tex]E(R)=I-E(C)=1,050-0.654\cdot 100=1,050-65.4=984.6[/tex]
Round your answer to the nearest hundredth.
B
35°
6
A
Someone help pls!
factoriza C (x) 42x4 − 36x2 + 24x + 12
Answer:
factor out 12
[tex]12(14cx - 5 + 2x)[/tex]
Cherry Trees: Timber yield is approximately equal to the volume of a tree, however, this value is difficult to measure without first cutting the tree down. Instead, other variables, such as height and diameter, may be used to predict a tree's volume and yield. Researchers wanting to understand the relationship between these variables for black cherry trees collected data from 31 such trees in the Allegheny National Forest, Pennsylvania. Height is measured in feet, diameter in inches (at 54 inches above ground), and volume in cubic feet. (Hand, 1994)Estimate Std. Error t value P(>|t|)(Intercept) -57.99 8.64 -6.71 0.00height 0.34 0.13 2.61 0.01diameter 4.71 0.26 17.82 (c) Are each of the predictors, "height" and "diameter" significant predictors of volume? PICK ONEOnly diameter is a significant predictor since it has the smallest p-valueYes, since the p-values associated with each predictor are less than 0.05No, since the p-values associated with each predictor are less than 0.05(d) How much volume is expected from a tree that measures 79 feet tall and has a diameter of 11.3 inches?(please round to the nearest cubic foot)________ cubic feet(e) A tree in the data set measures 79 feet tall, has a diameter of 11.3 inches, and is 24.2 cubic feet in volume. Determine whether the model gives an overestimate or underestimate of the volume of this tree. PICK ONEoverestimateunderestimate
Answer:
(c) Yes, since the p-values associated with each predictor are less than 0.05
(d) 22.093 cubic feet
(e) underestimate
Step-by-step explanation:
Our main objective is to determine the following
(c) Are each of the predictors, "height" and "diameter" significant predictors of volume? PICK ONE Only diameter is a significant predictor since it has the smallest p-value
Yes, since the p-values associated with each predictor are less than 0.05
No, since the p-values associated with each predictor are less than 0.05
Assuming our significance level ∝ = 0.05
From the data given;
p-value for height is = 0.00
p - value for diameter = 0.01
where, p-value ( = 0.01 and 0.00 ) < ∝ (= 0.05 )
Hence, according to the rejection rule; the null hypothesis is rejected and the predictors "height" and " diameter" are significant predictors of volume.
Thus
The answer is :
Only diameter is a significant predictor since it has the smallest p-value
Yes, since the p-values associated with each predictor are less than 0.05
(d) How much volume is expected from a tree that measures 79 feet tall and has a diameter of 11.3 inches?(please round to the nearest cubic foot)________
[tex]\hat y = -57.99+ 0.34 \ \mathbf{height }+4.71 \ \mathbf{diameter}[/tex]
[tex]\hat y = -57.99+ 0.34 \ \mathbf{(79)}+4.71 \ \mathbf{(11.3)}[/tex]
[tex]\hat y = 22.093 \ cubic foot[/tex]
(e)
A tree in the data set measures 79 feet tall, has a diameter of 11.3 inches, and is 24.2 cubic feet in volume. Determine whether the model gives an overestimate or underestimate of the volume of this tree. PICK ONE
overestimate
underestimate
We can posits that the model gives an underestimate of the volume of this tree due to the fact that the predicted value is 22.093 and which is less than the observed value of 24.2 cubic feet.
y - ( -3y ) what is the answer????
Answer:
4y
Step-by-step explanation:
y - -3y
Subtracting a negative is like adding
y+3y
Combine like terms
4y
Answer:
[tex]4y[/tex]
Step-by-step explanation:
[tex]y - ( - 3y) \\ y + 3y \\ = 4y[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Find the volume. Round your answer to one decimal place.
(PLZ SOMEBODY HELP ASAP)
Answer:
32.738ft³
32.7ft³
Step-by-step explanation:
This is half a sphere therefore volume=4/3πr³×1/2
4/3×22/7×2.5³×1/2
=32.738ft³
C. One half of the sum of six times a number and twenty-two
Answer:
Step-by-step explanation:
One half
Y is directly proportional to (x+2)2 when x=8 y=250 find y when x=4
Answer:
Y=150
Step-by-step explanation:
Just apply the proportionality rulw and solve for k. Then substitute the value of k into the equation.
Answer:
90
Step-by-step explanation:
Let the constant of proportionality be K
So that;
Y= K(x+2)^2
This means
For two corresponding points (x1,y1) and (x2,y2) we have;
Y1/(x1+2)^2= Y2/(x2+2)^2
If we consider x=8 y=250 as point (x1,y1) and y when x=4 as (x2,y2) we have ;
250/(8+2)^2 =y/(4+2)^2
250/(10)^2 = y/(6)^2
250/100 = y/36
250/100 × 36 = y
90= y
y=90
A bag contains four red, three green, and five yellow marbles. Three marbles are drawn,
One at time, without replacement. Determine the probability that the order in which they
are selected is(9A)
Ca) Yellow, red, green
(b) Yellow, green, green
(c) Yellow, Yellow, red
m how many ways can neople be selected from a group that consists of four adults a
what is the following quotient,
sqrt96/ sqrt8
Answer:
The answer is option 1.
Step-by-step explanation:
Firstly, you have to get rid of square root at the denorminator by multiply both side with √8 :
[tex] \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} [/tex]
[tex] \sqrt{a} \times \sqrt{a} = a[/tex]
[tex] \frac{ \sqrt{96} }{ \sqrt{8} } [/tex]
[tex] \frac{ \sqrt{96} }{ \sqrt{8} } \times \frac{ \sqrt{8} }{ \sqrt{8} } [/tex]
[tex] \frac{ \sqrt{96} \times \sqrt{8} }{ \sqrt{8} \times \sqrt{8} } [/tex]
[tex] \frac{ \sqrt{768} }{8} [/tex]
Next, you have to simply by looking which factor is a perfect square :
[tex] \frac{ \sqrt{256 \times 3} }{8} [/tex]
[tex] \frac{16 \sqrt{3} }{8} [/tex]
[tex]2 \sqrt{3} [/tex]
Answer:
its a
Step-by-step explanation:
on edge 2022
Tomas has two boxes to be shipped. One box weighs 3 \text{ kilograms}3 kilograms3, start text, space, k, i, l, o, g, r, a, m, s, end text. The other box weighs 720 \text{ grams}720 grams720, start text, space, g, r, a, m, s, end text.
Answer:
3.72kg
$29.76
See explanation below
Step-by-step explanation:
The question is incomplete as we are not told what we are to determine. Consider the following question
Question:
Tomas has two boxes to be shipped. One box weighs 3 kilograms. The other box weighs 720 grams.
a) What is the total weight of the boxes in kilogram?
b) If the shipping cost $8 per kilogram, what is the total cost of shipping.
Solution:
This is a question on measuring mass.
a) Total weight of the two boxes = weight of 1st box + weight of 2nd box
1st box = 3kg
2nd box = 720g
1000 g is equal to 1 kg
720g = (720/1000)kg = 0.72 kg
2nd box = 0.72 kg
Total weight of the two boxes = 3kg + 0.72kg
Total weight of the two boxes = 3.72kg
b) cost of shipping per kg = $8
cost of shipping for 3.72 kg = 8 × 3.72
Total cost of shipping for both boxes = $29.76
Answer: from my calculations its 3.72
which is also 3720 grams
