Answer:
7.5 minutes
Step-by-step explanation:
Given
See attachment for complete question
Let
[tex]t \to time[/tex]
[tex]y \to capacity[/tex]
From the question, we have the following points
[tex](t_1,y_1) = (0,7)[/tex] --- When he first sees it
[tex](t_2,y_2) = (3,5)[/tex] --- 3 minutes later
First, we calculate the rate (m)
[tex]m = \frac{y_2 -y_1}{t_2 -t_1}[/tex]
[tex]m = \frac{5 -7}{3 -0}[/tex]
[tex]m = -\frac{2}{3}[/tex]
The discharge rate is 2/3 gallons per minute
To calculate the additional minute, we simply consider the capacity of the tank at the later time. i.e. 5 gallons
To calculate time (t), we have:
[tex]Rate * Time = Capacity[/tex]
[tex]\frac{2}{3} * t = 5[/tex]
Solve for t
[tex]t = 5 *\frac{3}{2}[/tex]
[tex]t = \frac{15}{2}[/tex]
[tex]t = 7.5[/tex]
solve for x please !URGENT!
Answer:
It is x=908.
Might be wrong tho so dont jump me
Answer: 908
Step-by-step explanation:
x/4 = 89 + 138
x/4 = 227
x = 227 x 4
x = 908
Gillian swears her computations for the
following equations prove they do not
intersect. Her brother who just finished
learning about intersecting lines told her they
definitely intersect because the slopes are
different. Gillian remembered that logic from
class and then decided she needed to be able
to prove intersection by using algebra.
Although there are multiple strategies, how
might she prove intersection without graphing
of the following equations?
4x +3y = 6 and 6x + 2y = 10
Step-by-step explanation:
Given
Two lines are [tex]4x+3y=6[/tex] and [tex]6x+2y=10[/tex]
Two lines [tex]a_1x+b_1y=c_1[/tex] and [tex]a_2x+b_2y=c_2[/tex] will intersect when
[tex]\dfrac{a_1}{a_2}\neq \dfrac{b_1}{b_2}[/tex]
for the given lines
[tex]a_1=4,a_2=6,b_1=3,b_2=2[/tex]
[tex]\therefore \dfrac{4}{6}\neq \dfrac{3}{2}\\\\\dfrac{2}{3}\neq\dfrac{3}{2}[/tex]
Hence, lines are intersecting
If d(x) = x2 - 7x - 7, find d(x - 1).
Answer: x^2-9x+1
Step-by-step explanation:
x^2-7x-7 d(x-1)
(you would just replace x to (x-1)
(x-1)^2-7(x-1)-7
(solve by square rooting (x-1)(x-1) then foil)
x^2-9x+1
what is the probability of rolling a number that is greater than 4 on a number cube?
a.) 1/6
b.) 1/3
c.) 1/2
d.) 2/3
=========================================================
Explanation:
E = event space = {5,6}
The event space represents the set of all things we want to happen: namely rolling a 5 or a 6, since they are larger than 4.
S = sample space = {1,2,3,4,5,6}
The sample space is the set of all possible outcomes, whether we want them to happen or not. We have 6 possible outcomes.
Divide the number of items in each set
n(E) = 2
n(S) = 6
probability = n(E)/n(S) = 2/6 = 1/3
There's a 1 in 3 chance of rolling a number greater than 4.
Suppose that the width of a certain rectangle is 1 inch more than one-fourth of its length. The perimeter of the rectangle is 72 inches. Find the length and width of the rectangle.
Answer:
Length = 28 inches
Width = 8 inches
Step-by-step explanation:
Let length be L
Let Width be W
Given : W = 1 + (1/4)L
Perimeter = 2 x ( L + W)
[tex]72 = 2 (L + (1 + \frac{1}{4} L))\\\\36 = L + 1 + \frac{1}{4} L\\\\36 - 1 = \frac{5}{4} L\\\\35 = \frac{5}{4} L\\\\5L = 35 \times 4\\\\L = \frac{140}{5} = 28 \ in[/tex]
[tex]W = 1 + (\frac{1}{4} \times 28) = 1 + 7 = 8 \ in[/tex]
Find the 94th term of the arithmetic sequence -26, -37, -48
Answer:
-1049
Step-by-step explanation:
Let's assume it's a arithmetic sequence
a_1 = -26
d = a_2-a_1 = -11
==> a_94 = a_1+93*d = -1049
Answer:
-1071
Step-by-step explanation:
Let the common difference be 'd'.
d is 11
Find the difference from a (first term) and 11
Then use (n-1)
Angle Measurements 84 degree
Answer:
yes angle measures 84°as they are alternate angles
How many marble do you need to balance to scale
A. 4
B. 3
C. 2
D. 1
Answer: its B.
Step-by-step explanation:
have a good day hope this help
Answer:
B.3
Step-by-step explanation:
just divide 6 by 2
A-container holds 6 cups of yogurt the nutrion label reads that a serving size is 1/3 cups how many servings are in the cointaner
Answer:
1/3 = 1 serving
2/3 =2 servings
1 cup= 3 servings
so if one cup is 3 servings we can multiply 3 x 6 for an answer of 18 servings
From a stick 2y metres long, I cut a piece of length 4y centimetres. What fraction of the original stick remains?
Answer: [tex]\dfrac{49}{50}[/tex]
Step-by-step explanation:
Given
Length of the stick is [tex]2y\ m[/tex]
A piece of [tex]4y\ cm[/tex] is cut
We know, 1 m=100 cm
So, [tex]2y\ m[/tex] in cm is [tex]200y\ cm[/tex]
Remaining length after cut is
[tex]\Rightarrow 200y-4y=196y[/tex]
Fraction of length that is left after the cut is
[tex]\Rightarrow \dfrac{196y}{200y}\\\\\Rightarrow \dfrac{49}{50}[/tex]
Thus, [tex]\frac{49}{50}[/tex] fraction of original stick remains after cut
Given csc(A) = 65/16 and that angle A is in Quadrant I, find the exact value of sec A in simplest radical form using a rational denominator . Someone please help me!
Answer:
[tex]secA = \frac{65}{63}[/tex]
Step-by-step explanation:
[tex]cosec A = \frac{65}{16}\\\\sin A = \frac{1}{cosecA} = \frac{16}{65}\\\\cos^2 A = 1 - sin^2 A[/tex]
[tex]= 1 - (\frac{16}{65})^2\\\\=\frac{4225-256}{4225}\\\\=\frac{3969}{4225}\\[/tex]
[tex]cos A = \sqrt{\frac{3696}{4225}} = \frac{63}{65}[/tex]
[tex]secA = \frac{1}{cosA} = \frac{65}{63}[/tex]
Zx5+3 please help me
Use the Distributive Property to expand
the expression:
2 (y + 5x - 3)
subtract 8x-8y+9 from 5x-8y-z
Let z be inversely proportional to the cube root of y. When y =.064, z =3
a) Find the constant of proportionality k.
b) Find the value of z when y = 0.125.
Given:
z be inversely proportional to the cube root of y.
When y =0.064, then z =3.
To find:
a) The constant of proportionality k.
b) The value of z when y = 0.125.
Solution:
a) It is given that, z be inversely proportional to the cube root of y.
[tex]z\propto \dfrac{1}{\sqrt[3]{y}}[/tex]
[tex]z=k\dfrac{1}{\sqrt[3]{y}}[/tex] ...(i)
Where, k is the constant of proportionality.
We have, z=3 when y=0.064. Putting these values in (i), we get
[tex]3=k\dfrac{1}{\sqrt[3]{0.064}}[/tex]
[tex]3=k\dfrac{1}{0.4}[/tex]
[tex]3\times 0.4=k[/tex]
[tex]1.2=k[/tex]
Therefore, the constant of proportionality is [tex]k=1.2[/tex].
b) From part (a), we have [tex]k=1.2[/tex].
Substituting [tex]k=1.2[/tex] in (i), we get
[tex]z=1.2\dfrac{1}{\sqrt[3]{y}}[/tex]
We need to find the value of z when y = 0.125. Putting y=0.125, we get
[tex]z=1.2\dfrac{1}{\sqrt[3]{0.125}}[/tex]
[tex]z=\dfrac{1.2}{0.5}[/tex]
[tex]z=2.4[/tex]
Therefore, the value of z when y = 0.125 is 2.4.
Proportional quantities are either inversely or directly proportional. For the given relation between y and z, we have:
The constant of proportionality k = 1.2, andWhen y = 0.125 , z = 2.4What is directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
[tex]p = kq[/tex]
where k is some constant number called constant of proportionality.
This directly proportional relationship between p and q is written as
[tex]p \propto q[/tex] where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n are two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n}[/tex]
or
[tex]n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n}\\\\or\\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
For the given case, it is given that:
[tex]z \propto \dfrac{1}{^3\sqrt{y}}[/tex]
Let the constant of proportionality be k, then we have:
[tex]z = \dfrac{k}{^3\sqrt{y}}[/tex]
It is given that when y = 0.064, z = 3, thus, putting these value in equation obtained above, we get:
[tex]k = \: \: ^3\sqrt{y} \times z = (0.064)^{1/3} \times (3) = 0.4 \times 3 = 1.2[/tex]
Thus, the constant of proportionality k is 1.2. And the relation between z and y is:
[tex]z = \dfrac{1.2}{^3\sqrt{y}}[/tex]
Putting value y = 0.0125, we get:
[tex]z = \dfrac{1.2}{^3\sqrt{y}}\\\\z = \dfrac{1.2}{(0.125)^{1/3} } = \dfrac{1.2}{0.5} = 2.4[/tex]
Thus, for the given relation between y and z, we have:
The constant of proportionality k = 1.2, andWhen y = 0.125 , z = 2.4Learn more about proportionality here:
https://brainly.com/question/13082482
What is the measure of KPN?
Answer:
angle KPN=95 degree
Step-by-step explanation:
angle KPN = angle JPO (because they are vertically opposite angles)
Now,
angle JPO+angle LOP=180 degree(being co interior angles)
angle JPO + 85 =180
angle JPO =180-85
angle JPO =95
since angle JPO is equal to KPN ,angle KPN is 95 degree
Peter gets 1 star for every 3 correct answers he gets on khan academy. What is the minimum number of correct answers Peter must enter if he wants to get 12 stars?
For full points you need to write an equation that uses a variable and division, show what work you did to solve it, and then give me a final answer.
Answer:
Peter needs to get 36 problems correct to get 12 stars
Step-by-step explanation:
for every 3 correct answers, Peter gets 1 star
1/3
if he wants 12 stars he will have to get 'x' amount of questions correctly
considering this is constant, 1/3 will have to equal 12/x
[tex]\frac{1}{3} = \frac{12}{x} \\\\1x = 36\\[/tex]
1x = x, so you don't need to do anything to 36
therefore the answer is that you need to get 36 problems correct to get 12 stars
Max bought three items for $18.95 each and two items for $26.71 each. How much change would he get from $500 ?
Answer:
$389.73 in change
Step-by-step explanation
500-( (18.95 x 3)+(26.71 x 2) )=
500-(56.85+53.42)=
500-110.27=
389.73
There are 5 red, 4 blue, and 3 green marbles in a bag. What are the odds of randomly pulling a blue marble out of the bag and then randomly pulling a green marble out of the bag? The blue marble is NOT replaced.
A - 7/2
B - 12/24
C - 1/12
D - 1/11
Eddie bought 3 train tickets 17.00 each. If he paid with three $20 bills, how much change did Eddie receive?
Answer:
Step-by-step explanation:
Think of it as if he paid for each ticket with one $20 bill.
He gets $3 change from each one so his total change is $(
It costs $198.00 to buy beef to make 300 meatballs. What will the cost be
to make 120 meatballs?
Answer:$181.81
Step-by-step explanation:300/198
=1.5151515….multiple by 120
=181.818181
Chuck performed an experiment with a list of shapes. He randomly chose a shape from the list and recorded the results in the frequency table. The list of shapes and the frequency table are given below. Find the experimental probability of a parallelogram being chosen.
Answer:
1/6 (simplified)
Step-by-step explanation:
It's 3/18, but in most cases you should simplify unless it says to not.
help solving inequalities true or false (middle school) first person to answer i’ll give brainliest please!!!
Answer:
aef true and bcd false
hope u get well in your exams
Step-by-step explanation:
help pls.preparing for my term exam
Jackie is making flower arrangements. She has 2 roses and 4 daisies. If Jackie
wants to make all the arrangements identical and have no flowers left over, what
is the greatest number of flower arrangements she can make?
pls help <3
Answer:
2
Step-by-step explanation:
she will have 2 arangments of one rose and two daisies.
Answer:
2
Step-by-step explanation:
group off the daisies and rose
2 Rose's
4 raises
in order to make it identical
group 1 consist of ( 1 rose and 2 daisies)
group 2 consist of (1 rose and 2 daises)
only 2 bouquets
Pedro y su socia Karina vendieron 520 calendarios en el mes de Diciembre. Pedro vendió 120 calendarios más que su socia. ¿Cuántos calendarios vendió cada uno?
Answer:
Pedro vendió = 320 calendarios
Katrina vendió = 200 calendarios
Step-by-step explanation:
Dejemos que el número de calendarios
Pedro vendió = x
Katrina vendió = y
Pedro y su compañera Karina vendieron 520 calendarios en diciembre.
x + y = 520 .... Ecuación 1
Pedro vendió 120 calendarios más que su socio.
x = y + 120
Sustituimos y + 120 por x
y + 120 + y = 520
2 años = 520 - 120
2 años = 400
y = 400/2
y = 200 calendarios
Resolviendo para x
x = y + 120
x = 200 + 120
x = 320 calendarios
Por lo tanto,
Pedro vendió = 320 calendarios
Katrina vendió = 200 calendarios
The total surface area of a cube is 433.5 cm2.
Find its volume.
Answer:
Step-by-step explanation:
The area of 1 face is s^2
The area of 6 faces is 6s^2
6s^2 = 433.5 Divide by 6
s^2 = 433.5 / 6
s^2 = 72.25 Take the square root of both sides
sqrt(s^2) = sqrt(72.25)
s = 8.5
Normally you would find the volume of parallelepiped by using L * W * H
Since L W and H are all equal in a cube, the volume = s^3
S^3 = 8.5^3 = 614.125
The estimated daily living costs for an executive traveling to various major cities follow. The estimates include a single room at a four-star hotel, beverages, breakfast, taxi fares, and incidental costs. Click on the datafile logo to reference the data. City Daily Living Cost ($) City Daily Living Cost ($) Bangkok 242.87 Mexico City 212.00 Bogota 260.93 Milan 284.08 Cairo 194.19 Mumbai 139.16 Dublin 260.76 Paris 436.72 Frankfurt 355.36 Rio de Janeiro 240.87 Hong Kong 346.32 Seoul 310.41 Johannesburg 165.37 Tel Aviv 223.73 Lima 250.08 Toronto 181.25 London 326.76 Warsaw 238.20 Madrid 283.56 Washington, D.C. 250.61 a. Compute the sample mean (to 2 decimals). b. Compute the sample standard deviation (to 2 decimals). c. Compute a confidence interval for the population standard deviation (to 2 decimals).
Answer:
[tex]\bar x = 260.1615[/tex]
[tex]\sigma = 70.69[/tex]
The confidence interval of standard deviation is: [tex]53.76[/tex] to [tex]103.25[/tex]
Step-by-step explanation:
Given
[tex]n =20[/tex]
See attachment for the formatted data
Solving (a): The mean
This is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x = \frac{242.87 +212.00 +260.93 +284.08 +194.19 +139.16 +260.76 +436.72 +355.36 +.....+250.61}{20}[/tex]
[tex]\bar x = \frac{5203.23}{20}[/tex]
[tex]\bar x = 260.1615[/tex]
[tex]\bar x = 260.16[/tex]
Solving (b): The standard deviation
This is calculated as:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
[tex]\sigma = \sqrt{\frac{(242.87 - 260.1615)^2 +(212.00- 260.1615)^2+(260.93- 260.1615)^2+(284.08- 260.1615)^2+.....+(250.61- 260.1615)^2}{20 - 1}}[/tex][tex]\sigma = \sqrt{\frac{94938.80}{19}}[/tex]
[tex]\sigma = \sqrt{4996.78}[/tex]
[tex]\sigma = 70.69[/tex] --- approximated
Solving (c): 95% confidence interval of standard deviation
We have:
[tex]c =0.95[/tex]
So:
[tex]\alpha = 1 -c[/tex]
[tex]\alpha = 1 -0.95[/tex]
[tex]\alpha = 0.05[/tex]
Calculate the degree of freedom (df)
[tex]df = n -1[/tex]
[tex]df = 20 -1[/tex]
[tex]df = 19[/tex]
Determine the critical value at row [tex]df = 19[/tex] and columns [tex]\frac{\alpha}{2}[/tex] and [tex]1 -\frac{\alpha}{2}[/tex]
So, we have:
[tex]X^2_{0.025} = 32.852[/tex] ---- at [tex]\frac{\alpha}{2}[/tex]
[tex]X^2_{0.975} = 8.907[/tex] --- at [tex]1 -\frac{\alpha}{2}[/tex]
So, the confidence interval of the standard deviation is:
[tex]\sigma * \sqrt{\frac{n - 1}{X^2_{\alpha/2} }[/tex] to [tex]\sigma * \sqrt{\frac{n - 1}{X^2_{1 -\alpha/2} }[/tex]
[tex]70.69 * \sqrt{\frac{20 - 1}{32.852}[/tex] to [tex]70.69 * \sqrt{\frac{20 - 1}{8.907}[/tex]
[tex]70.69 * \sqrt{\frac{19}{32.852}[/tex] to [tex]70.69 * \sqrt{\frac{19}{8.907}[/tex]
[tex]53.76[/tex] to [tex]103.25[/tex]
Which value cannot represent the probability of an event occurring
Answer:
zero
Step-by-step explanation:
everything is theoretically possible
What statement is NOT true about the pattern shown below? 2/3, 4/6, 8/12, 16/24 Choices: Each fraction is greater than the previous fraction. Each fraction is equal to the previous fraction in the pattern multiplied by 2/2 Each fraction is equivalent to 2/3 The next fraction in the pattern is 32/48. Plsss help me out I need the answer like, rn. (That means SAY THE ANSWER RIGHT NOW!)
Answer: Each fraction is greater than the previous fraction.
Step-by-step explanation:
The fractions given are:
2/3, 4/6, 8/12, 16/24
Note that
2/3 = 4/6 = 8/12 = 16/32
The Fractions are all equal. Each fraction is equivalent to 2/3
The pattern used here is:
2/3 × 2/2 = 4/6
4/6 × 2/2 = 8/12
8/12 × 2/2 = 16/24
16/24 × 2/2 = 32/48
Each fraction is equal to the previous fraction in the pattern multiplied by 2/2
Also, the next fraction in the pattern is 32/48.
The statement that "Each fraction is greater than the previous fraction" is incorrect. The fractions are all equal.
Hello please help asap, thanks!
Answer:
Last image.
Step-by-step explanation:
So, we know that the orginal graph is of [tex]\sqrt[7]{x}[/tex]
We need to find the graph of [tex]-\sqrt[7]{x}-8[/tex]
First off, we see a negative in front of the root.
This means that all the values will be flipped across the x axis.
This removes the first two answer graphs, for they are of the postive root.
Next, we have a -8 following the root.
So, when another number is inside of the root(example: [tex]\sqrt[7]{x-6}[/tex]) You are going to add 6 to the x axis, basically shifting everything to the right(postive). If it was a postive 6 inside the root, we would move it left(negative)
This is not what is being done in our graph, I just wanted to explain this for future graphing.
Now, when a number is outside the root, such as the one above, then it shifts the y axis. In this case we have a -8 outside the root. This means that the graph will be shifted down(negative) by 8.
This eliminates the 3rd graph image, leaving the last graph answer shown below.
Hope this helps!