Answer:
A lies along the positive x-axis and B lies along negative x - axis .
Step-by-step explanation:
They tell us that we have two vectors, A and B. And they give us a series of conditions for this, now, what would be the correct possibility.
A lies along the positive x-axis and B lies along negative x - axis .
This is because when both vectors will be in x axis but opposite to each other, then the angle between them will be 180 ° and cos180 ° is -1.
Convert 3 over 7 into a percent.
Step-by-step explanation: To write a fraction as a percent, first remember that a percent is a ratio of a number to 100.
So to write 3/7 as a percent, we need to find a fraction
equivalent to 3/7 that has a 100 in the denominator.
We can do this by setting up a proportion.
So we have [tex]\frac{3}{7} = \frac{n}{100}[/tex].
Now, we can use cross-products to find the missing value.
So we have (3)(100) which is 300 is equal to (7)(n) or 7n.
So we have the equation 300 = 7n.
Next, dividing both sides of the equation by 7, we have 42.8571 = n.
So 3/7 is equal to 42.8571/100 or 42.8571%.
A boy has 27 cubes, each with sides the length of 1cm. He uses these cubes to build one big cube. What is the volume of the big cube?
Answer:54
volume:side*side*side
side:1 cm*1 cm *1 cm
answer=icm
Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. Find the tax rate t that maximizes revenue for the government. (Round your answer to three decimal places.)
S(t) = 7 â 6(cubedroot(t))
Answer:
66.992%
Step-by-step explanation:
[tex]Sales, S(t)=7-6\sqrt[3]{t}[/tex]
Since we want to maximize revenue for the government
Government's Revenue= Sales X Tax Rate
[tex]R(t)=t \cdot S(t)\\R(t)=t(7-6\sqrt[3]{t})\\=7t-6t^{1+1/3}\\R(t)=7t-6t^{4/3}[/tex]
To maximize revenue, we differentiate R(t) and equate it to zero to solve for its critical points. Then we test that this critical point is a relative maximum for R(t) using the second derivative test.
Now:
[tex]R'(t)=7-6*\frac{4}{3} t^{4/3-1}\\=7-8t^{1/3}[/tex]
Setting the derivative equal to zero
[tex]7-8t^{1/3}=0\\7=8t^{1/3}\\t^{1/3}=\dfrac{7}{8} \\t=(\frac{7}{8})^3\\t=0.66992[/tex]
Next, we determine that t=0.6692 is a relative maximum for R(t) using the second derivative test.
[tex]R''(t)=-8*\frac{1}{3} t^{1/3-1}\\R''(t)=-\frac{8}{3} t^{-2/3}[/tex]
R''(0.6692)=-3.48 (which is negative)
Therefore, t=0.66992 is a relative maximum for R(t).
The tax rate, t that maximizes revenue for the government is:
=0.66992 X 100
t=66.992% (correct to 3 decimal places)
Please answer this correctly
Answer:
2/3
Step-by-step explanation:
Total sides = 6
Number 5 and all even numbers = 1+3
=> 4
P(5 or even ) = 4/6
=> 2/3
Two bond funds pay interest at rates that differ by 4%. Money invested for one year in the first fund earns $550 interest. The same amount invested in the other fund earns $770. Find the lower rate of interest. _________ %
Answer:
10% interest.
Step-by-step explanation:
Interest I = PRT/100
If the rate R = x% we have
550 = P*x *1 / 100
and
770 = P*(x + 4) * 1 / 100
so From first equation
Px = 55000 and from the second
Px + 4P = 77000
So Px = 77000 - 4P
Therefore 77000 - 4P = 55000
4P = 22000
P = 5,500
So x = 55000/5500 = 10%.
And the rate for the other fund is 10 + 4 = 14%.
After the last ice age began, the number of animal species in Australia changed rapidly. The relationship between the elapsed time, t, in years, since the ice age began, and the total number of animal species, S year(t), is modeled by the following function: S year(t)=25,000,000⋅(0.78)t Complete the following sentence about the rate of change in the number of species in decades. Round your answer to two decimal places. Every decade, the number of species decays by a factor of
Answer:
Every decade, the number of species decays by a factor of 0.0834.
Step-by-step explanation:
Let be [tex]S(t) = 25,000,000\cdot 0.78^{t}[/tex], [tex]\forall t \geq 0[/tex]. The decay rate per decay is deducted from the following relation:
[tex]\frac{S(t+10)}{S(t)} = \frac{25,000,000\cdot 0.78^{t+10}}{25,000,000\cdot 0.78^{t}}[/tex]
[tex]\frac{S(t+10)}{S(t)} = 0.78^{t+10-t}[/tex]
[tex]\frac{S(t+10)}{S(t)} = 0.78^{10}[/tex]
[tex]\frac{S(t+10)}{S(t)} = 0.0834[/tex]
Every decade, the number of species decays by a factor of 0.0834.
Answer:
28% subtracted
Step-by-step explanation:
khan
Cheryl bought 3.4 pounds of coffee that cost $6.95 per pound . How many did she spend on coffee
Answer:
23.63
Step-by-step explanation:
multiply the cost by the pounds
Answer:
$23.63
Step-by-step explanation:
3.4 X 6.95 = 23.63
which three lengths could be the lengths of the sides of a triangle?
21 cm, 7 cm, 6 cm
12 cm 5 cm 17 cm
9 cm 22 cm, 11 cm
10cm 25cm, 24cm.
Answer:
None of the sides can be a triangle.
Step-by-step explanation:
simplify 2(4+8)÷2(8+8)
192.
2(8+4)÷2(8+8) = 1(4+8)×(8+8)
1×12×16=192.
Answer:
192Step-by-step explanation:
[tex]2(4 + 8) \div 2(8 + 8)[/tex]
Any expression divided by itself equals 1
[tex]1(4 +8) \times (8 + 8)[/tex]
Add numbers
[tex]1 \times 12 \times 16[/tex]
Any expression multiplied by 1 remains the same
[tex]12 \times 16[/tex]
Multiply the numbers
[tex]192[/tex]
Hope this helps...
Good luck on your assignment..
helppppppp pleassssseeeeee
Answer:
First blank is 4, second blank is 0
Step-by-step explanation:
divide it :)
Answer:
Yellow box #1=0
Yellow box #1=4
Step-by-step explanation:
The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. (Give answers to 2 decimal places) Store's Card Major Credit Card
Sample size 64 49Sample mean $140 $125Population variance $100 $641. A point estimate for the difference between the mean purchases of the users of the two credit cards is:________.2. At 95% confidence, the margin of error is:____________.3. A 95% confidence interval estimate for the difference between the average purchases of the customers using the two different credit cards is___ to ___.
4. The test statistic for an alpha of .05 is:____________.
Answer:
Step-by-step explanation:
1) Point estimate is the difference between the sample means. Therefore,
A point estimate for the difference between the mean purchases of the users of the two credit cards is = 140 - 125 = $15
2) Margin of error = z√(σ²/n1 + σ2²/n2)
Where
z is the z score from the 95% confidence level. From the normal distribution table, z = 1.96
s1 and s2 are standard deviation for both customers respectively.
Standard deviation = √variance
σ1 = √100 = 10
σ2 = √641 = 25.32
Margin of error = 1.96√(10²/64 + 25.32²/49 = 7.5
At 95% confidence, the margin of error is 7.5
3) The confidence interval for the difference of two population means is expressed as point estimate ± margin of error
Confidence interval = 15 ± 7.5
The upper boundary for the confidence interval is
15 - 7.5 = 7.5
The lower boundary for the confidence interval is
15 + 7.5 = 22.5
A 95% confidence interval estimate for the difference between the average purchases of the customers using the two different credit cards is $7.5 to $22.5
4) Since the population standard deviations are known, we would use the formula to determine the test statistic(z score)
z = (x1 - x2)/(√σ1²/n2 + σ2²/n2)
z = (140 - 125)/√10²/64 + 25.32²/49
z = 1.02
The test statistic for an alpha of .05 is 1.02
The Ericsson method is one of several methods claimed to increase the likelihood of a baby girl. In a clinical trial, results could be analyzed with a formal hypothesis test with the alternative hypothesis of pgreater than0.5,which corresponds to the claim that the method increases the likelihood of having a girl, so that the proportion of girls is greater than 0.5. If you have an interest in establishing the success of the method, which of the following P-values would you prefer: 0.999, 0.5, 0.95, 0.05, 0.01, 0.001? Why?
Answer:
0.001
Step-by-step explanation:
Here, the aim is to support the null hypothesis, Ha. Where Ha: p > 0.5. Which means we are to reject null hypothesis H0. Where H0: p = 0.5.
The higher the pvalue, the higher the evidence of success. We know If the pvalue is less than level of significance, the null hypothesis H0 is rejected.
Hence the smallest possible value 0.001 is preferred as the pvalue because it corresponds to the sample evidence that most strongly supports the alternative hypothesis that the method is effective
You want to buy a $200000 home. You plan to pay 10% as a down payment, and take out a 30 year loan for the rest. A. How much is the loan amount going to be?
B. What will your monthly payments be if the interest rate 5%?
C. What will your monthly payments be if the interest rate is 6%?
Answer:
A = 20,000
Step-by-step explanation:
200,000 ÷ 10 = 20,000
The loan amount going to be for a home that cost $200000 home. You plan to pay 10% as a down payment and take out a 30-year loan for the rest is $180000.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
The cost of the house, C = $200000,
The time = 30 years,
If the down payment is 10% then the remaining amount,
Down payment amount, D = 10% of 2000000 = $20000
Remaining amount = C - D
Remaining amount = $200000 - $20000 = $180000,
Therefore, the loan amount is $180000.
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From a group of 10 women and 15 men, a researcher wants to randomly select
women and men for a study in how many ways can the study group be selected?
O A 17,876
78,016,400
OG 105, 102,625
OD 00,000,000
WO
Answer:
The total number of ways the researcher can select 5 women and 5 men for a study is 7,56,756.
Step-by-step explanation:
The complete question is:
From a group of 10 women and 15 men, a researcher wants to randomly select 5 women and 5 men for a study in how many ways can the study group be selected?
Solution:
In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.
The formula to compute the combinations of k items from n is given by the formula:
[tex]{n\choose k}=\frac{n!}{k!\cdot (n-k)!}[/tex]
The number of women in the group: [tex]n_{w}=10[/tex].
The number of women the researcher selects for the study, [tex]k_{w}=5[/tex]
Compute the total number of ways to select 5 women from 10 as follows:
[tex]{n_{w}\choose k_{w}}=\frac{n_{w}!}{k_{w}!\cdot (n_{w}-k_{w})!}=\frac{10!}{5!\cdot (10-5)!}=\frac{10!}{5!\times 5!}=252[/tex]
The number of men in the group: [tex]n_{m}=15[/tex].
The number of men the researcher selects for the study, [tex]k_{m}=5[/tex]
Compute the total number of ways to select 5 men from 15 as follows:
[tex]{n_{m}\choose k_{m}}=\frac{n_{m}!}{k_{m}!\cdot (n_{m}-k_{m})!}=\frac{15!}{5!\cdot (15-5)!}=\frac{15!}{5!\times 10!}=3003[/tex]
Compute the total number of ways the researcher can select 5 women and 5 men for a study as follows:
[tex]{n_{w}\choose k_{w}}\times {n_{m}\choose k_{m}}=252\times 3003=756756[/tex]
Thus, the total number of ways the researcher can select 5 women and 5 men for a study is 7,56,756.
Add. Answer as a fraction. Do not include spaces in your answer. Do not include spaces in your answer.
Answer: 49/9
Step-by-step explanation: 42/9 + 7/9 = 49/9
Make first fraction into improper fraction with the same common dominator as 7/9 and add them both
Hope this helps:)
Answer:
49/9
Step-by-step explanation:
Which of the following statements must be true about this diagram? Check all that apply.
Answer:
Options (D), (E) and (F) are the correct options.
Step-by-step explanation:
From the figure attached,
1). Angle 4 is the exterior angle of the given triangle having interior angles 1, 2 and 3.
Therefore, by the property of exterior angle,
∠4 = ∠1 + ∠2
2). Since ∠4 = ∠1 + ∠2,
Therefore, ∠4 will be greater than ∠1
Similarly, ∠4 will be greater than ∠2
Therefore, Options (D), (E) and (F) are the correct options.
Use the properties of logarithms to prove log81000= log210.
Answer:
Step-by-step explanation:
Given the expression [tex]log_81000 = log_210[/tex], to prove this expression is true using the properties of logarithm, we will follow the following steps.
Starting from the Left Hand Side:
[tex]log_81000\\[/tex]= log₈ 10³= log_ 2^3 (10³)= log₂10Explain in your own words why a polynomial can’t be a quadratic if a= 0?
If [tex]a = 0[/tex], then [tex]y = ax^2+bx+c[/tex] turns into [tex]y = 0x^2+bx+c[/tex]. That [tex]0x^2[/tex] term goes away because it turns into 0, and adding 0 onto anything does not change the expression.
So [tex]y = 0x^2+bx+c[/tex] turns into [tex]y = bx+c[/tex] which is a linear equation (b is the slope, c is the y intercept). It is no longer a quadratic as quadratic equations always graph out a curved parabola.
As an example, you could graph out [tex]y = 0x^2+3x+4[/tex] and note how it's the exact same as [tex]y = 3x+4[/tex], both of which are straight lines through the two points (0,4) and (1,7).
A scooter runs 40 km using 1 litre of petrol tje distance covered by it using 15/4 litres of petrol is
Answer:
150 km
Step-by-step explanation:
1 liter ............ 40 km
15/4 liter .........x km
x = 15/4×40/1 = 600/4 = 150 km
Please answer this correctly
Answer:
12.5%
Step-by-step explanation:
There is only 1 seven card from the 8 total cards.
1 out of 8.
1/8 = 0.125
P(7) = 12.5%
Answer:
12.5%
Step-by-step explanation:
Total Cards = 8
Number 7 = 1
P(7) = 1/8
In %age:
=> 12.5%
Algebra 1 help. I got A
Answer: A
Step-by-step explanation:
(f-g)(x) means f(x)-g(x). Since we are given f(x) and g(x), we can directly subtract them.
4x+1-(x²-5) [distribute -1]
4x+1-x²+5 [combine like terms]
4x-x²+6 [rewrite in the order of exponents]
-x²+4x+6
what's 3 - 3 x 6 + 2
Answer:
-13
Step-by-step explanation:
John is going for a walk. He walks for 6.4 miles at a speed of 2 miles per hour. For how many hours does he walk?
Answer:
t = d/s
t = 6.4 / 2 miles
t = 3.2 miles
Step-by-step explanation:
follow me plzzz
Please answer this correctly
Answer:
50%
Step-by-step explanation:
There are 3 numbers fitting the rule, 1, 2, and 6. There is a 3/6 chance rolling one of them or 50%.
Answer:
50%
Step-by-step explanation:
1 value> 5 and 2 values<3, out of total of 6
P (greater than 5 or less than 3) = 3/6= 50%
Susan can pick 4 pounds of coffee beans in an hour or gather 2 pounds of nuts. Tom can pick 2 pounds of coffee beans in an hour or gather 4 pounds of nuts. Each works 6 hours per day. a. Together, what is the maximum number of pounds of coffee beans the two can pick in a day
Answer:
144
Step-by-step explanation:
Susan can pick 4 pounds of coffee beans in an hour. Tom can pick 2 pounds of coffee beans in an hour. Together, they can pick 6 pounds of coffee an hour.
4 + 2 = 6
There are 24 hours in a day. Multiply the time by the amount that can be picked to find the answer.
24 × 6 = 144
Together, the maximum number of pounds of coffee beans the can pick in a day is 144 pounds.
Together they can pick a maximum of 36 pounds of coffee
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
given:
Susan can pick 4 pounds of coffee or 2 pounds of nuts.
Tom can pick 2 pounds of coffee or 4 pounds of nuts.
So, In 6 hours
Susan will pick
= 4 * 6
= 24 pounds of coffee.
In 6 hours,
Tom will pick
=2 * 6
= 12 pounds of coffee.
Hence, together they can pick a maximum of 36 pounds of coffee
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A family has a phone plan that includes 4 GB of data per month. 10 days into a 30-day month, the family has used 1 GB. At that rate, how many GB will the family use for the entire month?
Answer:
3 GB
Step-by-step explanation:
Since the family has used 1 GB in 10 days. With the same rate in 30 days they would have 3 GB
What is the domain of the relation graphed below?
Answer:
domain: (-4,4)
Step-by-step explanation:
i'm not sure if it has brackets because it doesn't have point that are on x-intervals -4 and 4
the table shows the time it took a group of students to complete a puzzle
Answer:
Where is the table because I dont see it up here?
A 4-ft-high and 7-ft-wide rectangular plate is submerged vertically in water so that the top is 1 ft below the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Recall that the weight density of water is 62.5 lb/ft3).
Total depth of the bottom of the plate is 4 + 1 = 5
Force = limit(5,1) 62.5 *7* x * dx
= 437.5. Lim(5,1) x*dx
= 437.5(x^2/2)^5 , 1
= 437.5 x (5^2/2 - 1/2)
= 437.5 x 12
= 5,250 pounds
The hydrostatic force against one side of the plate will be 5250 pounds.
What is hydrostatic force?The force exerted by the water of surface is known as hydrostatic force.
A 4-ft-high and 7-ft-wide rectangular plate is submerged vertically in water so that the top is 1 ft below the surface.
[tex]\rm Force = \int^5_1 62.5 *7* x * dx\\\\\\ Force = 437.5 \left [ \dfrac{x^2}{2} \right]^5_1\\\\\\Force = 218.75 \left [ x^2 \right]^5_1\\\\[/tex]
Solve the equation further, we have
Force = 218.75 x (5² – 1²)
Force = 218.75 x 24
Force = 5,250 pounds
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When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support capital punishment? Number of individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The calculated value for the test statistic equals a. 20. b. 4. c. 2. d. -2.
Answer:
[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
The expected values for all the categories is :
[tex] E_i =\frac{150}{3}=50[/tex]
And then the statistic would be given by:
[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]
And the best option would be:
b. 4
Step-by-step explanation:
For this problem we have the following observed values:
Yes 40 No 60 No Opinion 50
And we want to test the following hypothesis:
Null hypothesis: All the opinions are uniformly distributed
Alternative hypothesis: Not All the opinions are uniformly distributed
And for this case the statistic would be given by:
[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
The expected values for all the categories is :
[tex] E_i =\frac{150}{3}=50[/tex]
And then the statistic would be given by:
[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]
And the best option would be:
b. 4