The total number of votes would be: 7752 total votes.
Here's how you solve it!
For every 3 yes there was 5 no's.
You would but that into a fraction so it would be 3/5
Then you take the number of no votes and multiply.
3/5 x 4845
Then you would get 2907.
4845+ 2907= 7752
4845= no votes
2907= yes votes
7752= total votes
Hope this helps! :3
A radioactive substance decays by x % each day. After 8 days half of the substance has decayed. Find the value of x. Give your answer to 1 decimal place.
Answer:
8.3
Step-by-step explanation:
Let Ao be the original amount and A the amount after t days.
Then we have the exponential function
A = Ao(1 - x)^t or
A/Ao = (1 - x)^t
When t = 8, A/Ao = 0.5
0.5 = (1 - x)^8
(0.5)^(1/8) = 1 - x
0.917 = 1 - x
x = 1 - 0.917 = 0.083 = 8.3 %
The substance decays by 8.3 % each day.
Beth wants to plant a garden at the back of her house. She has 32m of fencing. The area that can be enclosed is modelled by the function A(x) = -2x2 + 32x, where x is the width of the garden in metres and A(x) is the area in square metres. What is the maximum area that can be enclosed?
Please help :(
Answer:
The maximum area that can be obtained by the garden is 128 meters squared.
Step-by-step explanation:
A represents area and we want to know the maximum.
[tex]A(x)=-2x^2+32x[/tex] is a parabola. To find the maximum of a parabola, you need to find it's vertex. The y-coordinate of the vertex will give us the maximum area.
To do this we will need to first find the x-coordinate of our vertex.
[tex]x=\frac{-b}{2a}{/tex] will give us the x-coordinate of the vertex.
Compare [tex]-2x^2+32x[/tex] to [tex]ax^2+bx+c[/tex] then [tex]a=-2,b=32,c=0[tex].
So the x-coordinate is [tex]\frac{-(32)}{2(-2)}=\frac{-32}{-4}=8[/tex].
To find the y that corresponds use the equation that relates y and x.
[tex]y=-2x^2+32x[/tex]
[tex]y=-2(8)^2+32(8)[/tex]
[tex]y=-2(64)+32(8)[/tex]
[tex]y=-128+256[/tex]
[tex]y=128[/tex]
The maximum area that can be obtained by the garden is 128 meters squared.
By using the vertex formula to find the width that maximizes the area of Beth's garden, we determine that the maximum area she can enclose with 32 meters of fencing is 128 square meters when the width is set to 8 meters.
The question is about finding the maximum area that can be enclosed by Beth with 32 m of fencing for a garden, modeled by the function A(x) = -2x2 + 32x, where x is the width of the garden in meters. To find the maximum area, we need to determine the vertex of this quadratic equation since the coefficient of x2 is negative, indicating a maximum point for the area.
To find the vertex, we can use the formula x = -b / 2a, where a and b are the coefficients from the quadratic equation A(x). Thus, x = -32 / (2*(-2)) = 8 meters. Substituting x back into the function to find the maximum area, A(8) = -2(8)2 + 32(8) = -128 + 256 = 128 square meters.
This shows that the maximum area Beth can enclose with 32 meters of fencing for her garden is 128 square meters, by setting the width to 8 meters.
Find the sum of the vectors <7,−2> and <1,8>. Then find the magnitude and direction of the resultant vector. Round angles to the nearest degree and other values to the nearest tenth.
Answer:
The sum of the vectors is <8 , 6>
The magnitude of the resultant vector is 10
The direction of the resultant vector is 37°
The answer is the 1st answer: <8 , 6> ; 10 ; 37°
Step-by-step explanation:
* Lets explain how to solve the problem
∵ The first vector is <7 , -2>
∵ The second vector is <1 , 8>
∴ The sum of the 2 vectors = <7 , -2> + <1 , 8>
∴ Their sum = <7 + 1 , -2 + 8> = <8 , 6>
* The sum of the vectors is <8 , 6>
- The magnitude of the resultant vector = √(x² + y²)
∵ x = 8 and y = 6
∴ The magnitude of the resultant vector = √(8² + ²)
∴ The magnitude of the resultant vector = √(36 + 64) = √100 = 10
* The magnitude of the resultant vector is 10
- The direction of the vector = tan^-1 (y/x)
∵ x = 8 and y = 6
∴ The direction of the vector = tan^-1 (6/8) = 36.869 ≅ 37°
* The direction of the resultant vector is 37°
Answer:
The answer is A. ⟨8, 6⟩; 10; 37°
Based on the graph, which of the following statements is true?
A. The number of cupcakes depends on the total price.
B. The total price depends on the number of boxes.
C. The total price depends on the number of cupcakes.
D. The number of boxes depends on the total price.
Answer:
B) Total price of cakes depend on the number of boxes.
Step-by-step explanation:
Given: Graph
To find : Based on the graph, which of the following statements is true.
Solution : We have given graph between total price of cupcakes and number of boxes.
We can see from the graph is linear graph that is straight line graph passing through the origin.
It shows the Directly relation between total price of cakes and number of boxes.
Number of boxes ∝Total price of cakes.
So, Total price of cakes depend on the number of boxes.
Therefore, B) Total price of cakes depend on the number of boxes.
Find the x-intercept of the line 3x - 9y = 15.
Answer:
The x-intercept is 5.
Some people prefer you right it as a point (5,0).
Step-by-step explanation:
The x-intercept can be found by setting y=0 and solving for x.
Just like to find the y-intercept you can set x=0 and solve for y.
Let's find the x-intercept.
So we will set y=0 and solve for x:
3x-9y=15
3x-9(0)=15
3x-0 =15
3x =15
Divide both sides by 3:
x =15/3
x =5
So the x-intercept is (5,0).
Using the graph of f(x) and g(x), where g(x) = f(k⋅x), determine the value of k.
A.) 3
B.) 1/3
C.) -1/3
D.) -3
Answer:
A.) 3
Step-by-step explanation:
In the equation g(x) = f(k·x), the factor k is a horizontal compression factor. Here the graph of g is the graph of f compressed by a factor of 3.
The point (3, 2) on the graph of f(x) becomes the point (1, 2) on the graph of g(x). The point (1, 2) is a factor of 3 closer to the y-axis than the point (3, 2).
It may be easier to think of k as the reciprocal of the horizontal expansion (dilation) factor. The function g is horizontally dilated by a factor of 1/3 from function f, so k = 1/(1/3) = 3.
To determine the value of k, we need to analyze the graphs of f(x) and g(x). By comparing the graphs, we can determine if k is greater or less than 1. The graph of g(x) is compressed horizontally, indicating that k is less than 1.
Explanation:To determine the value of k, we need to analyze the relationship between the functions f(x) and g(x).
Since g(x) = f(k⋅x), we can compare the graphs of f(x) and g(x) to find the value of k.
If k is greater than 1, the graph of g(x) will be compressed horizontally compared to the graph of f(x).
If k is less than 1, the graph of g(x) will be stretched horizontally compared to the graph of f(x).
By analyzing the graphs of f(x) and g(x), we can see that the graph of g(x) is compressed horizontally, indicating that k is less than 1.
Therefore, the value of k is B.) 1/3.
What is the intersection of the three sets: A = {0, 2, 3, 6, 8}, B = {2, 3, 6, 8, 9}, and C = {1, 2, 4, 8, 9}? A. {2, 8, 9} B. {2, 6, 8} C. {2, 8} D. {0, 1, 2, 3, 4, 6, 8, 9}
Answer:
{2,8}
Step-by-step explanation:
This is the same thing as asking what element (in this case what number) is in all 3 sets.
0 isn't in all 3 sets because it isn't in B.
2 is in all 3 sets
3 isn't because it isn't in C
4 isn't in A.
6 isn't in C.
8 is in all 3 sets.
9 isn't in A
So the elements that are in the 3 sets are {2,8}.
Aziza has a triangle with two sides measuring 11 in. And 15 in. She claims that the third side can be any length as long as it is greater than 4 in. Which statement about Aziza's claim is correct?
Answer:
The third side can be any length as long as it is greater than 4 in and less than 26 in
Step-by-step explanation:
we know that
The Triangle Inequality Theorem, states that The sum of the lengths of any two sides of a triangle is greater than the length of the third side
Let
x ----> the length of the third side
Applying the triangle inequality theorem
1) 11+15 > x
26 > x
rewrite
x < 26 in
2) 11+x > 15
x> 15-11
x > 4 in
therefore
Aziza's claim is incomplete
The third side can be any length as long as it is greater than 4 in and less than 26 in
Answer:
Aziza’s claim is not correct. The third side must be between 4 in. and 26 in.
Step-by-step explanation:
A partial proof was constructed given that MNOP is a parallelogram. By the definition of a parallelogram, MN ∥ PO and MP ∥ NO. Using MP as a transversal, ∠M and ∠P are same-side interior angles, so they are supplementary. Using NO as a transversal, ∠N and ∠O are same-side interior angles, so they are supplementary. Using OP as a transversal, ∠O and ∠P are same-side interior angles, so they are supplementary. Therefore, __________ and _________ because they are supplements of the same angle. Which statements should fill in the blanks in the last line of the proof?
∠M is supplementary to ∠N; ∠M is supplementary to ∠O
∠M is supplementary to ∠O; ∠N is supplementary to ∠P
∠M ≅ ∠P; ∠N ≅ ∠O
∠M ≅ ∠O; ∠N ≅ ∠P
Answer:
∠M ≅ ∠O; ∠N ≅ ∠PStep-by-step explanation:
According to the problem
[tex]\angle N + \angle O =180\°[/tex]
[tex]\angle O + \angle P = 180\°[/tex]
[tex]\angle M + \angle P = 180\°[/tex]
Which means,
[tex]\angle N + \angle O = \angle O + \angle P\\\angle N = \angle P[/tex]
And,
[tex]\angle O + \angle P = \angle M + \angle P\\\angle O = \angle M[/tex]
Therefore, the right answer is the last choice.
Find the area of the shaded region under the standard distribution curve.
A. 2.5000
B. 0.9452
C. 0.1841
D. 0.7611
Answer:
D. 0.7611
Step-by-step explanation:
The area is:
P(z<1.60) − P(z<-0.90)
Looking up the values in a z-score table:
0.9452 − 0.1841
0.7611
Answer:
D. 0.7611
Step-by-step explanation:
We have been given a graph of a normal standard distribution curve. We are asked to find the area of the shaded region under the given standard distribution curve.
The area of the shaded region under the standard distribution curve would be area of a z-score of 1.60 minus area of a z-score of [tex]-0.90[/tex] that is [tex]P(-0.90<z<1.60)=P(z<1.60)-P(z<-0.90)[/tex]
Using normal distribution table, we will get:
[tex]P(-0.90<z<1.60)=0.94520-0.18406[/tex]
[tex]P(-0.90<z<1.60)=0.76114[/tex]
Therefore, the shaded area under the curve is 0.7611 and option D is the correct choice.
Use the diagram to find the measure of the given angle.
Select one:
a. 110
b. 120
c. 130
d. 140
mDAF
Answer:
c. 130
Step-by-step explanation:
∠FAB is a vertical angle with the one that is marked, so is 50°. ∠FAE is the complement of that, so is 40°. ∠DAF is the sum of the right angle DAE and angle FAE, so is ...
90° + 40° = 130° = m∠DAF
The summer reading list for your English class has twelve books, and the list for History has eight books. You need to read three books for English and two books for History. How many different sets of books can you read?
Answer:
Step-by-step explanation:
This is a combination problem from stats. We have a total of 12 English books from which you have to 3. The order in which you pick them doesn't matter, you only need to determine how many different combinations are available to you. This is the combination formula, then:
₁₂C₃ = [tex]\frac{12!}{3!(12-3)!}[/tex]
I'm just going to simplify the right side and leave off the left side til the end of the algebra because it's easier. The right side simplifies to
[tex]\frac{12*11*10*9!}{3*2*1*9!}[/tex]
The 9!'s cancel each other out, leaving you with
[tex]\frac{12*11*10}{3*2*1}=\frac{1320}{6}[/tex]
Therefore,
₁₂C₃ = 220 possible different combinations of English books from which to pick.
We'll do the same for History, which has a combination formula that looks like this:
₈C₂= [tex]\frac{8!}{2!(8-2)!}[/tex]
That right side expands to
[tex]\frac{8*7*6!}{2*1*6!}[/tex]
The 6!'s cancel each other out, leaving you with:
[tex]\frac{8*7}{2*1}=\frac{56}{2}[/tex]
Therefore,
₈C₂ = 28 possible different combinations of History books from which to pick.
You may or may not need to add those together to get the answer your teacher is looking for.
[25 points] Help with proportions, I don't understand! 134 out of 205 families in "Chimgan" village keep cows, 142 keep sheep and 76 keep goats. 67 families have cows and sheep, 10 have cows and goats, 15 have sheep and goats. There are 34 families who keep all three kinds of pets. a) How many families keep only one kind of pet?
b) How many have no pets at all? Hint: Use the following diagram.
Answer:
only keeps-
cows=134-67-34-10=23
sheep=142-67-34-15=26
goats=76-10-34-15=17
no pets=205-23-17-26-67-10-16-34
Step-by-step explanation:
some have one pets some have two or three
total no. of family have cows is 134 then 134 minus by those with more will be no. of family only with cows
The Pacific Ocean is divided into two sets of gyres, in the _____ and _____. A. East Pacific; West Pacific B. North Pacific; East Pacific C. South Pacific; West Pacific D. North Pacific; South Pacific
Answer:
North pacific and south pacific.
Step-by-step explanation:
D.
The Pacific Ocean's two major gyre systems are found in the North Pacific and South Pacific.
Explanation:The Pacific Ocean is divided into two sets of gyres, notably in the North Pacific and South Pacific. Gyres are large systems of circulating ocean currents; the gyres in the Pacific Ocean play significant roles in influencing climate and marine life. The North Pacific Gyre, encircling the area between Asia and North America, and the South Pacific Gyre, contained mostly between Australia, South America and Antarctica, are the two main gyre systems in the Pacific Ocean.
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what is the answer to 13p12=
Answer:
156p
Step-by-step explanation:
13p×12
multiply the numbers
= 156p
The value of the permutation [tex]^{13}P_{12}[/tex] is 6,227,020,800.
We have,
To calculate [tex]^{13}P_{12}[/tex], we need to determine the value of 13 factorial (13!) divided by (13 - 12) factorial (1!).
The formula for factorial is n! = n * (n - 1) * (n - 2) * ... * 2 * 1.
So,
[tex]^{13}P_{12}[/tex]
= 13!/1!
= 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2
= 6,227,020,800.
Therefore,
The value of the permutation [tex]^{13}P_{12}[/tex] is 6,227,020,800.
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Jasmine is saving to buy a bicycle. The amount she has saved is shown in the table. What is the function describes the amount A, in dollars, Jasmine has saved after t weeks?
Table
Weeks/Amount
1 / $30
2 / $45
3 / $60
4 / $75
5 / $90
6 / $105
Answer:
A = 15t +15
Step-by-step explanation:
The amounts have a common difference of $15, so that is apparently the amount Jasmine is saving each week. Week 1, however, is $15 more than $15×1. The function ...
A = 15t +15 . . . . dollars
seems to fit the data.
When taking a 12 question multiple choice test, where each question has 3 possible answers, it would be unusual to get _____ or more questions correct by guessing alone.
Assuming pure chance, on a 12 question multiple choice test with 3 options per question, it would be unusual to get 5 or more questions correct by guessing alone.
Explanation:The question pertains to the probability of guessing correctly on a multiple-choice test with 3 options per question, assuming pure chance. On a 12-question test, the probability of guessing correctly on a single question is 1/3. Hence, for 12 questions, the expected number of correct guesses would be the total number of questions times the probability of getting each question right, which is 12 * 1/3 = 4. Therefore, it would be unusual to get 5 or more questions correct by guessing alone.
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In a 12-question multiple choice test with 3 possible answers for each, a student randomly guessing is expected to get roughly 4 correct answers. Getting 6 or more questions correct by random guessing would be considered unusual.
Explanation:When taking a 12-question multiple choice test where each question has 3 possible answers, the probability of getting a question correct by simply guessing is 1/3. Here, we want to calculate the unusual scenario of how many or more questions correct by simply guessing.
If we apply the principle of probability, under normal circumstances where guessing is purely random, the expected number of correct answers would be the total number of questions times the probability of getting a question correct. This equates to 12 × (1/3) which is 4 correct answers. This means on average, if the student were to guess all their answers, they are likely to get around 4 correct answers.
However, getting 6 or more questions right by guessing alone would be considered unusual due to the low probability of guessing correct answers repeatedly. Keep in mind, that these calculations hold if all the guesses are random and there is no elimination of wrong answers based on known information.
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The length of country and western songs is normally distributed and has a mean of 170 seconds and a standard deviation of 40 seconds. Find the probability that a random selection of 16 songs will have mean length of 158.30 seconds or less. Assume the distribution of the lengths of the songs is normal.
Answer: 0.1210
Step-by-step explanation:
Given : The length of country and western songs is normally distributed with [tex]\mu=170 \text{ seconds}[/tex]
[tex]\sigma=40\text{ seconds}[/tex]
Sample size : [tex]n=16[/tex]
Let x be the length of randomly selected country song.
z-score : [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z=\dfrac{158.30-170}{\dfrac{40}{\sqrt{16}}}\approx-1.17[/tex]
The probability that a random selection of 16 songs will have mean length of 158.30 seconds or less by using the standard normal distribution table will be
= [tex]P(x\leq158.30)=P(z\leq-1.17)[/tex]
[tex]=0.1210005\approx0.1210[/tex]
Hence, the probability that a random selection of 16 songs will have mean length of 158.30 seconds or less is 0.1210
The probability that a random selection of 16 country and western songs will have a mean length of 158.30 seconds or less is approximately 12.10%. This is calculated using the concept of the Sampling Distribution of the Mean and a Z score.
Explanation:To find the probability that a random selection of 16 songs will have a mean length of 158.30 seconds or less, we need to use the concept of the Sampling Distribution of the Mean. This is a statistical concept that involves probabilities and the distribution of sample means. We assume that the distribution of length of songs is normal.
In our case, the population mean (μ) is 170 seconds and the population standard deviation (σ) is 40 seconds. We are looking at samples of 16 songs, so the sample size (n) is 16.
The mean of the sampling distribution of the mean (also just the population mean) is μ. The standard deviation of the sampling distribution (often called the standard error) is σ/√n. Given our numbers, this would be 40/√16 = 10.
We want the probability that the sample mean is 158.30 or less. The Z score is a measure of how many standard errors our observed sample mean is from the population mean. To find the Z score we use the formula: Z = (X - μ) / (σ/√n).
Therefore: Z = (158.30 - 170) / 10 = -1.17
A Z score of -1.17 corresponds to a probability of about 0.1210 or 12.10% that a random selection of 16 songs will have a mean length of 158.30 seconds or less.
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Find the sum of the series of the arithmetic series:
7 + 13 + . . . + 601
a. 182,704
b. 60,800
c. 30,400
d. 15,200
[tex]\bf 7~~,~~\stackrel{7+6}{13}......601\qquad \qquad \stackrel{\textit{common difference}}{d = 6} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=7\\ d=6\\ a_n=601 \end{cases} \\\\\\ 601=7+(n-1)6\implies 601=7+6n-6\implies 601=1+6n \\\\\\ 600=6n\implies \cfrac{600}{6}=n\implies 100=n \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{sum of a finite arithmetic sequence} \\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ \cline{1-1} a_1=7\\ a_n=601\\ n=100 \end{cases}\implies S_{100}=\cfrac{100(7+601)}{2} \\\\\\ S_{100}=\cfrac{60800}{2}\implies S_{100}=30400[/tex]
(PLEASE HELP)
Two trains leave the station at the same time, one heading west and the other east. The westbound train travels at 55 miles per hour. The eastbound train travels at 75 miles per hour. How long will it take for the two trains to be 208 miles apart?
Do not do any rounding.
Answer:
1.6 hours or 1 hour 36 minutes.
Step-by-step explanation:
The rate at which the trains are moving apart is 55 + 75 = 130 mph.
Speed = distance / time so:
130 = 208 / t
130t = 208
t = 1.6 hours.
Which numbers are rational numbers and irrational numbers and why
..................................__
-3.786, 3π, 8/17, 8.23, √11, 10.86731234, 0.75, √.49
Answer:
rational: -3.786, 8/17, 8.23, 10.86731234, 0.75, √.49 = 0.7
irrational: 3π, √11
Step-by-step explanation:
Any number that can only be represented completely using symbols, such as π or √, is an irrational number.
If the number can be expressed as the ratio of two integers, it is a rational number. Such numbers include proper and improper fractions, integers, any number you can write with a finite number of digits, and any repeating decimal, regardless of the length of the repeat.
A rancher wants to fence in an area of 3,000,000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?
Answer:
shortest length of fence is 8485.2 ft
Step-by-step explanation:
Given data
area = 3,000,000 square feet
to find out
shortest length of fence
let length L and width is W
so area is L × W
W = 3 × [tex]10^{6}[/tex] /L ............1
2W = 6 × [tex]10^{6}[/tex] /L
rectangular field and then divide it in half
so fencing will be 3 × L + 2 × W
i.e. 3 L + 2W
fencing = 3 L + 6 × [tex]10^{6}[/tex] /L
fencing minimum = 3 L - 6 × [tex]10^{6}[/tex] /L²
fencing minimum length will be zero
3 L - 6 × [tex]10^{6}[/tex] /L² = 0
3 L² = 6 × [tex]10^{6}[/tex]
L² = 2 × [tex]10^{6}[/tex]
L = 1414.2
so from equation 1
W = 3 × [tex]10^{6}[/tex] /L
W = 3 × [tex]10^{6}[/tex] /1414.2
W = 2121.3
so fencing will be 3 L +2 W
so fencing = 3 × 1414.2 +2 × 2121.3
fencing = 4242.6 +4242.6
fencing = 8485.2
shortest length of fence is 8485.2 ft
The shortest length of fence the rancher can use is approximately 6104 feet. This is derived by setting up the area and perimeter equations, differentiating to find the minimum perimeter, and substituting the values back into the equation.
Explanation:This problem is a basic optimization problem in mathematics. Given that the area of the field to be fenced is 3,000,000 square feet, we can use the formula for the area of a rectangle, which is length multiplied by width. Since the rancher wants to divide the field in two with a fence running parallel to one side, the total amount of fencing will be two lengths and three widths.
Let's denote the length of the rectangle as 'l' and the width as 'w'. The area is thus l*w = 3,000,000. The perimeter is defined as 2*l + 3*w. Given that the area is fixed, w can be expressed in terms of l as 3,000,000/l.
Therefore, the perimeter becomes 2*l + 3*(3,000,000/l). The minimum fence length or perimeter occurs when the derivative of this equation is zero. By differentiating and setting the equation to zero, we get l=sqrt(1,500,000), approximately 1224.74 feet. Substituting this value into the equation for w gives us w also as 1224.74 feet.
The shortest length of fence that the rancher can use is thus 2*l + 3*w = 2*1224.74 + 3*1224.74 = 6103.7 feet.
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What are the foci of the hyperbola whose equation is (x-6)^2/16-(y+7)^2/9 = 1?
(1,−7) and (11,−7)
(2,−7) and (10,−7)
(6,−12) and (6,−2)
(6,−10) and (6,−4)
Answer: (1, -7) (11, -7)
Step-by-step explanation:
The foci of the hyperbola whose equation is (1,−7) and (11,−7).
What are the foci of a hyperbola?The hyperbola is horizontal, we will count 5 spaces left and right and plot the foci there.
We need to use the formula [tex]\rm c^ 2 =a^ 2 +b^ 2[/tex] to find c.
The given equation of the hyperbola is;
[tex]\rm \dfrac{(x-6)^2}{16}-\dfrac{(y+7)^2}{9}=1[/tex]
Here a^2 is 16 and b^2 =9.
Substitute all the values in the formula
[tex]\rm c^ 2 =a^ 2 +b^ 2\\\\\rm c^ 2 16+9\\\\\rm c^2=25\\\\c^2=5^2\\\\c=5[/tex]
The center of the hyperbola is (6, -7).
The foci of the hyperbola whose equation is;
( 6 +5 , -7), (6-5, -7)
(11, -7), (1, -7)
Hence, the foci of the hyperbola whose equation is (1,−7) and (11,−7).
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A sample of 4 cards is selected without replacement from a standard deck of 52-cards, in which there are 26 red and 26 black cards. Let X be the number of cards that are red. (A) Binomial(B) Not binomial
Answer:
(B) this is not binomial function
Step-by-step explanation:
Given data
sample card n = 4 cards
total card number N = 52 cards
red card = 26
black card = 26
to find out
X be the number of cards that are red. (A) Binomial(B) Not binomial
solution
we know that 4 is selected with out replacement from 52 cards
we can say that R item is as success , here R is Red card
so that 52 - R items will be as failures
and we know
failure = 52 - 26 = 26 that is equal to 26 black card
we know this is Hyper geometric function
so this is not binomial function
Which equation shows a valid, practical step in solving
For this case we have the following equation:
[tex]\sqrt [4] {2x-8} + \sqrt [4] {2x + 8} = 0[/tex]
If we subtract both sides of the equation [tex]\sqrt [4] {2x + 8}[/tex] we have:
[tex]\sqrt [4] {2x-8} = - \sqrt [4] {2x + 8}[/tex]
To eliminate the radical we raise both sides of the equation to the fourth power:
[tex](\sqrt [4] {2x-8}) ^ 4 = (- \sqrt [4] {2x + 8}) ^ 4[/tex]
Answer:
Option D
Suppose your grandfather earned a salary of $12,000 in 1964. If the CPI is 31 in 1964 and 219 in 2016, then the value of your grandfather's salary in 2016 dollars is approximately
The value of a salary of $12,000 in 1964 would be approximately $84,000 in 2016 dollars when adjusted for inflation as measured by the Consumer Price Index.
Explanation:To calculate the value of your grandfather's salary in 2016 dollars, the relative rates of Consumer Price Index (CPI) for both years need to be compared. The salary of $12,000 in 1964, adjusted for inflation through 2016, would be:
$12,000 * (219 / 31)
This formula indicates the change in CPI from 1964 to 2016 and multiplies it by the salary in 1964 dollars. Therefore, your grandfather's salary in 2016 is approximately $84,000 when accounting for inflation.
Learn more about Consumer Price Index here:https://brainly.com/question/4513076
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Final answer:
The value of your grandfather's salary in 2016 dollars is approximately $84,687.10
Explanation:
The value of your grandfather's salary in 2016 dollars is approximately $84,687.10
. To calculate this, you need to adjust the 1964 salary for inflation using the Consumer Price Index (CPI) for 1964 and 2016. First, find the inflation factor by dividing the CPI of 2016 by the CPI of 1964. Then, multiply the 1964 salary by this factor to get the equivalent value in 2016 dollars.
Which out of the 2 choices is correct ?
Answer:
sinB is correct
Step-by-step explanation:
Calculating each of cos/ sin for ∠B
cosB = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{3\sqrt{5} }[/tex] = [tex]\frac{2}{\sqrt{5} }[/tex] and
[tex]\frac{2}{\sqrt{5} }[/tex] × [tex]\frac{\sqrt{5} }{\sqrt{5} }[/tex] = [tex]\frac{2\sqrt{5} }{5}[/tex] ≠ [tex]\frac{\sqrt{5} }{5}[/tex]
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sinB = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{3\sqrt{5} }[/tex] = [tex]\frac{1}{\sqrt{5} }[/tex] and
[tex]\frac{1}{\sqrt{5} }[/tex] × [tex]\frac{\sqrt{5} }{\sqrt{5} }[/tex] = [tex]\frac{\sqrt{5} }{5}[/tex]
Answer:sinB is correct
Step-by-step explanation
Step-by-step explanation:
Calculating each of cos/ sin for ∠B
cosB = = = and
× = ≠
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sinB = = = and
× =
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Suppose u and v are a basis for the two-dimensional vector space V. Prove that w = u+v and x = u-v is also a basis. Hint: If two vectors form a basis, then any vector in the space can be expressed as linear combinations of the two vectors. You know that u and v are a basis. Pick any vector, call it s, in the space and check that you can always do the same using w and x.
Answer with Step-by-step explanation:
We are given that u and v are a basis for the two dimensional vector space.
To prove that w=u+v and x=u-v is also a basis .
By using matrix we prove w and x are basis of vector space.
We make a matrix from w and x
[tex]\left[\begin{array}{cc}1&1\\1&-1\end{array}\right][/tex]
Apply operation
[tex] R_1\rightarrow R_1-R_2[/tex]
[tex]\left[\begin{array}{cc}0&2\\1&-1\end{array}\right][/tex]
Apply [tex] R_2\rightarrow R_2-+R_1[/tex]
[tex]\left[\begin{array}{cc}0&2\\1&1\end{array}\right][/tex]
Apply [tex]R_1\rightarrow \frac{1}{2}R_1[/tex]
[tex]\left[\begin{array}{cc}0&1\\1&1\end{array}\right][/tex]
Apply [tex]R_2\rightarrow R_2-R_1[/tex]
[tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right][/tex]
Rank is 2 .Therefore, row one and second row are linearly independent.
Hence, first and second row are linearly independent because, any row is not a linear combination of other row.
Therefore, w and x are formed basis of given vector space.
A 28,000-gallon swimming pool is being drained using a pump that empties 700 gallons per hour. Which equation models this situation if g is the number of gallons remaining in the pool and t is the amount of time in hours the pool has been draining? 28,000 = –700t 28,000g = –700t g = 700t – 28,000 g = 28,000 – 700t
Answer:
g = 28,000 - 700t
Step-by-step explanation:
This solution reads, in words,
"the amount of water remaining in the pool is equal to 28,000 gallons minus 700 gallons per hour", which is what your situation is asking you. You start with 28,000 gallons and are pumping out (subtracting) 700 gallons per hour.
g is what remains
Answer: [tex]g=28000-700t[/tex]
Step-by-step explanation:
Given : A 28,000-gallon swimming pool is being drained using a pump that empties 700 gallons per hour.
i.e, Remaining gallons = 28,000- 700 × Number of hours.
Let g be the number of gallons remaining in the pool and t is the amount of time in hours the pool has been draining.
Then, the equation models this situation will be :-
[tex]g=28000-700t[/tex]
Can u guys please identify the types of these triangles ( question 13)
Answer:
1_ scalene
2_isoscelous
Answer:
13a. scalene
13b. isosceles
13c. right
Step-by-step explanation:
i took geometry hope this helps