Answer:
[tex]y = \frac{5ct}{3b}[/tex]
Step-by-step explanation:
[tex]\frac{5t}{4y} =\frac{3b}{4c}[/tex]
1. start by multiplying y to both sides:
y × [tex]\frac{5t}{4y} =\frac{3b}{4c}[/tex] × y
[tex]\frac{5t}{4} =\frac{3b}{4c}y[/tex]
2. divide both sides by [tex]\frac{3b}{4c}[/tex]
[tex]\frac{5t}{4}/\frac{3b}{4c} =\frac{3b}{4c}y/\frac{3b}{4c}[/tex]
[tex]y = \frac{5ct}{3b}[/tex]
What do you know to be true about the values of p and ?
p"
q
601
454
45
A. p> 9
B. p<9
C. p= 9
D. Can't be determined
An arch is in the form of a parabola given by the function h = -0.06d^2 + 120, where the origin is at ground level, d meters is the horizontal distance and h is the height of the arch in meters.
Graph this function on your graphing calculator then complete the following statements.
The height of the arch is: ------- m
The width to the nearest meter, at the base of the arch is ------ m
Answer:
See attachment for graph
The height of the arch is: 120 m
The width to the nearest meter, at the base of the arch is 22 m
Step-by-step explanation:
Given
[tex]h = -0.06d^2 + 120[/tex]
Solving (a): The graph
See attachment for graph
Variable h is plotted on the vertical axis while variable d is plotted on the horizontal axis.
Solving (b): The height
The curve of [tex]h = -0.06d^2 + 120[/tex] opens downward. So, the maximum point on the vertical axis represents the height of the arch,
Hence:
[tex]height = 120[/tex]
Solving (c): The width
The curve touches the horizontal axis at two different points.
[tex]x_1 = -11[/tex]
[tex]x_2 = 11[/tex]
The absolute difference of both points represents the width.
So:
[tex]Width = |x_2 - x_1|[/tex]
[tex]Width = |11 - -11|[/tex]
[tex]Width = |11 +11|[/tex]
[tex]Width = |22|[/tex]
Hence:
[tex]Width = 22[/tex]
Can someone help me with this problem?
Question 5 Multiple Choice Worth 1 points)
(01.03 MC)
Bunny Hill Ski Resort charges $35 for ski rental and $10 an hour to ski. Black Diamond Ski Resort charges $40 for ski rental and $5 an hour to ski. Create an equation to determine at what point
the cost of both ski slopes is the same.
Answer:
Bunny Hill Ski Resort:
y = 10x + 35
Diamond Ski Resort:
y = 5x + 40
Point where the cost is the same:
(1, 45)
Step-by-step explanation:
The question tells us that:
$35 and $40 are initial fees
$10 and $5 are hourly fees
This means that x and y will equal:
x = number of hours
y = total cost of ski rental after a number of hours
So we can form these 2 equations:
y = 10x + 35
y = 5x + 40
Now we are going to use System of Equations to find what point the cost of both ski slopes is the same.
Because they both equal y, we can set the equations equal to each other:
10x + 35 = 5x + 40
And we use basic algebra to solve for x:
10x + 35 = 5x + 40
(subtract 5x from both sides)
5x + 35 = 40
(subtract 35 from both sides)
5x = 5
(divide both sides by 5)
x = 1
Remember, x equals the number of hours.
That means when your rent out the skis for 1 hour, you will get the same price of $45 (you find the price by plugging in 1 into both of the equations)
Hope it helps (●'◡'●)
Find the value of x in each case
The answer is 36 degrees
Step 1
Angle GEH=180-2x (angles on a a straight line are supplementary)
Step 2
4x= G^+GE^H(sum of exterior angle)
4x=x+(180-2x)
4x=180-x
4x+x=180
5x=180
x=36 degrees
please help i am stuck on this assignment
Answer:
answer
x = -13/ 15, 0
Step-by-step explanation:
15x^2 + 13 x = 0
or, x(15x + 13) = 0
either, x = 0
or, 15x + 13 = 0
x = -13/15
Answer:
The answer should be C...............
imma sorry if I'm wrong
Which of the following equations describes this graph?
A. y=(x-1)^2-
B. y=(x-3)^2+2
C. y=(x+1)^2-2
D. y=(x-2)^2+3
Answer:
The choose (A)
y=(x-1)²-2
find 9 rational no. between 8/7 and 17/10.
Answer:
[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]
Step-by-step explanation:
We need to find 9 rational number between [tex]\dfrac{8}{7}\ \text{and}\ \dfrac{17}{10}[/tex]
We make the denominators of both fractions same. So,
[tex]\dfrac{8}{7}\times \dfrac{10}{10}=\dfrac{80}{70}[/tex]
and
[tex]\dfrac{17}{10}\times \dfrac{7}{7}=\dfrac{119}{70}[/tex]
The rational number are:
[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]
the perimeter of a rectangle garden is 330 feet. If the length of the garden is 94 feet , what is its width ?
Answer:
71 feet
Step-by-step explanation:
94×2=188
330-188=142
142÷2=71
Lolz please help me I would gladly appreciate it
Pentagon has sum of 540°
A box contains 5 white balls, 3 black balls, and 2 red balls.A-What is the probability of drawing a white ball?B- How many white balls must be added to the box so that the probability of drawing a white ball is 3/4?C-How many black balls must be added to the original assortment so that the probability of drawing a white ball is 1/4?
Answer:
[tex](a)\ P(White) = \frac{1}{2}[/tex]
(b) 10 additional white balls
(c) 10 additional black balls
Step-by-step explanation:
Given
[tex]White = 5[/tex]
[tex]Black =3[/tex]
[tex]Red = 2[/tex]
Solving (a): P(White)
This is calculated as:
[tex]P(White) = \frac{White}{Total}[/tex]
[tex]P(White) = \frac{5}{5+3+2}[/tex]
[tex]P(White) = \frac{5}{10}[/tex]
[tex]P(White) = \frac{1}{2}[/tex]
Solving (b): Additional white balls, if [tex]P(White) = \frac{3}{4}[/tex]
Let the additional white balls be x
So:
[tex]P(White) = \frac{White+x}{Total+x}[/tex]
This gives:
[tex]\frac{3}{4} = \frac{5+x}{10+x}[/tex]
Cross multiply
[tex]30+3x = 20 + 4x[/tex]
Collect like terms
[tex]4x - 3x = 30 - 20[/tex]
[tex]x = 10[/tex]
Hence, 10 additional white balls must be added
Solving (c): Additional black balls, if [tex]P(White) = \frac{1}{4}[/tex]
Let the additional black balls be x
So:
[tex]P(White) = \frac{White}{Total+x}[/tex]
So, we have:
[tex]\frac{1}{4} = \frac{5}{10+x}[/tex]
Cross multiply
[tex]10+x = 5 * 4[/tex]
[tex]10+x = 20[/tex]
Collect like terms
[tex]x = 20 -10[/tex]
[tex]x = 10[/tex]
Hence, 10 additional black balls must be added
Plz help I’ll mark u
Answer:
SAS=side angle side
there is two side and one angle
Answer:
SAS theorem
explanation:
Can you help me answer this question? Screenshot is added.
9514 1404 393
Answer:
(c)
Step-by-step explanation:
[tex]\displaystyle\sqrt[3]{xy^5}\sqrt[3]{x^7y^{17}}=\sqrt[3]{x^{1+7}y^{5+17}}=\sqrt[3]{x^6x^2y^{21}y}=\sqrt[3]{x^6y^{21}}\sqrt[3]{x^2y}\\\\=\boxed{x^2y^7\sqrt[3]{x^2y}}[/tex]
Allie rode her bike up a hill at an average speed of 12 feet/second. She then rode back down the hill at an average speed of 60 feet/second. The entire trip took her 2 minutes. What is the total distance she traveled. [Hint: use t = time traveling down the hill]
Answer:
The total distance Allie traveled was 0.81 miles.
Step-by-step explanation:
Since Allie rode her bike up a hill at an average speed of 12 feet / second, and she then rode back down the hill at an average speed of 60 feet / second, and the entire trip took her 2 minutes, to determine what is the total distance she traveled, the following calculation must be performed:
12 + 60 = 72
72 x 60 = 4320
1000 feet = 0.189394 miles
4320 feet = 0.8181818 miles
Therefore, the total distance Allie traveled was 0.81 miles.
PLEASE HELLPP!!! Choose the best graph that represents the linear equation:
-x = 2y + 1
Graph A
On a coordinate plane, a line goes through (negative 1, 0) and (1, negative 1).
Graph B
On a coordinate plane, a line goes through (negative 3, negative 1) and (1, 1).
Graph C
On a coordinate plane, a line goes through (1, 0) and (5, negative 2).
Graph D
On a coordinate plane, a line goes through (negative 3, negative 2) and (1, 0).
a.
Graph A
c.
Graph C
b.
Graph B
d.
Graph D
Please select the best answer from the choices provided
A
B
C
D
Answer:
C
Step-by-step explanation: just C-
Answer: Its not c
Step-by-step explanation: It is A
Find the solution for this system of equations.
2x + 4y = 8
x = 3y − 6
Answer:
[tex]{ \tt{2x + 4y = 8 - - - (a)}} \\ { \tt{x = 3y - 6 - - - (b)}} [/tex]
Substitute for x in equation (a) :
[tex]{ \tt{2(3y - 6) + 4y = 8}} \\ { \tt{6y - 12 + 4y = 8}} \\ { \tt{10y = 20}} \\ y = 2[/tex]
Substitute for y in equation (b) :
[tex]{ \tt{x = (3 \times 2) - 6}} \\ x = 0[/tex]
2x+4y =8
x=3y-6 ——> x–3y=–6
x–3y = – 6 ] ×(–2) ——> –2x +6y=12
2x+4y=8
–2x+6y =12
__o_o____
0+10y=20 —> 10y= 20 —> y= 20/10 —> y= 2
2x+4y=8 —> 2x + 4(2) = 8 —> 2x + 8=8 —> 2x = 0 —> x=0
(x,y) —> (0,2)
If the angles (4x + 4)° and (6x – 4)° are the supplementary angles, find the value of x.
Answer:
18
Step-by-step explanation:
Supplementary angles means sum of angles is 180.
4x + 4 + 6x - 4 = 180
4x + 6x + 4 - 4 = 180
10x = 180
x = 180 / 10
x = 18
Answer:
x=18 degree
Step-by-step explanation:
If they are supplementary angles, then their sum = 180 degree
4x+4 + 6x-4 =180
4x+6x + 4-4 = 180
10x = 180
x=180/10
x=18
solve the inequality x(x+6) >16
please show steps and interval notation!
Answer:
x > 2, x < -8
Interval notation:
( -infinity, -8) U (2, infinity)
Step-by-step explanation:
x(x+6) > 16
distribute x into x+6, multiply
x^2 + 6x > 16
bring 16 to left side, subtract
x^2 + 6x - 16 > 0
factors of -16 that add to +6 is -2 and +8
(x - 2)(x + 8) > 0
solve for x:
x < -8, x > 2
Interval notation:
( -infinity, -8) U (2, infinity)
One number is 1/4 of another number. The sum of the two numbers is 5. Find the two numbers. Use a comma to separate your answer
Answer: 1, 4
Step-by-step explanation:
Number #1 = xNumber #2 = [tex]\frac{1}{4} x[/tex][tex]\frac{1}{4} x+x=5\\\\\frac{1}{4} x+\frac{4}{4} x=5\\\\\frac{5}{4} x=5\\\\5x=4*5\\5x=20\\x=4[/tex]
Number #1 = x = 4Number #2 = [tex]\frac{1}{4} x[/tex] = [tex]\frac{1}{4} *4=\frac{4}{4} =1[/tex]The distribution of the number of apples trees a farmer can plant each day is bell-shaped and has a mean of 62 and a standard deviation of 8. Use the empirical rule to help you answer the following. What is the approximate percentage of trees planted between 38 and 68
Answer:
The empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 62, standard deviation of 8.
What is the approximate percentage of trees planted between 38 and 86?
38 = 62 - 3*8
86 = 62 + 3*8
So within 3 standard deviations of the mean, which, by the empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.
What is the solution to the linear equation?
-12 + 3b - 1 = -5 - b
Answer:
b=2
Step-by-step explanation:
Can someone please help me, with part B
Step-by-step explanation:
let y = x+5/4
Interchanging x and y , we get ;
x = y+5/4
or, 4x = y+5
or, 4x-5 = y
or, g(x) -1 = 4x-5
Answer:
In verse of B.g(x)=[tex]\frac{x+5}{4}[/tex] is:
4x-5
Answer:
Solution given:
B.g(x)=[tex]\frac{x+5}{4}[/tex]
let
g(x)=y
y=[tex]\frac{x+5}{4}[/tex]
Interchanging role of x and y
we get:
x=[tex]\frac{y+5}{4}[/tex]
doing crisscrossed multiplication
4x=y+5
y=4x-5
So
g-¹(x)=4x-5
On dividing 12x³ by 4x the quotient is …..
Answer:
12x^3 is equivalent to
12x*12x*12x which if we multiply is
1728x
we divide by 4x
1728x divided by 4x=432x
Hope This Helps!!!
Answer:
3x^2
Step-by-step explanation:
when u divide 12x^3/4x....u divide 12/4=3 along with the x also..tat is x^3/x=x^2
Suppose 46% of politicians are lawyers. If a random sample of size 662 is selected, what is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%
Answer:
0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose 46% of politicians are lawyers.
This means that [tex]p = 0.46[/tex]
Sample of size 662
This means that [tex]n = 662[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.46[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.46*0.54}{662}} = 0.0194[/tex]
What is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%?
p-value of Z when X = 0.46 + 0.04 = 0.5 subtracted by the p-value of Z when X = 0.46 - 0.04 = 0.42. So
X = 0.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.5 - 0.46}{0.0194}[/tex]
[tex]Z = 2.06[/tex]
[tex]Z = 2.06[/tex] has a p-value of 0.9803
X = 0.42
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.42 - 0.46}{0.0194}[/tex]
[tex]Z = -2.06[/tex]
[tex]Z = -2.06[/tex] has a p-value of 0.0197
0.9803 - 0.0197 = 0.9606
0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%
Jerome is cooking dinner. He needs 8 ounces of broccoli for each person. Part A: Jerome is not sure how many people will come to dinner. Write an expression with a variable that represents the amount of broccoli Jerome needs for dinner. Identify what the variable represents. Part B: If Jerome has 32 ounces of broccoli, how many people can he feed? Create an equation and show all work to solve it.
Answer:
A. 8x = amount of broccoli needed
B. 4 people; 32÷8=4
Step-by-step explanation:
A. the variable (x) represents the amount of people.
B. 32 ounces divided by 8 ounces is enough for four people.
which of the following is a geometric sequence -3,3,-3,3... 11,16,21,26, ... 6, 13, 19, 24, ... -2,6,14,22, ...
Answer:
p and q are two numbers.whrite down an expression of
* Insert a digit to make numbers that are divisible by 6 if it is possible:
234_6
Answer:
i put in 3 to make 23436 because 36 is divisible by 6
Coliform bacteria are randomly distributed in a river at an average concentration of 1 per 20cc of water. What is the variance of the number of Coliform bacteria in a sample of 40cc of water
Answer:
[tex]Var = 1.9[/tex]
Step-by-step explanation:
Given
[tex]p = \frac{1}{20}[/tex] i.e. 1 per 20cc of water
[tex]n = 40[/tex] -- sample size
Required
The variance
This is calculated using:
[tex]Var = np(1 - p)[/tex]
So, we have:
[tex]Var = 40 * \frac{1}{20} * (1 - \frac{1}{20})[/tex]
[tex]Var = 40 * \frac{1}{20} * \frac{19}{20}[/tex]
[tex]Var = 2 * \frac{19}{20}[/tex]
[tex]Var = \frac{38}{20}[/tex]
[tex]Var = 1.9[/tex]
A party supply company makes cone shaped party hats for children using thin cardboard. To the nearest square centimeter, how much cardboard is required to make the party hate use pie = 3.14.
Answer:
A. 754 cm²
Step-by-step explanation:
Amount of cardboard needed = surface area of the cone
Curved surface area of the cone = πrl
Where,
π = 3.14
r = ½(20) = 10 cm
l = 24 cm
Plug in the values into the formula
Curved surface area = 3.14 × 10 × 24 = 753.6 ≈ 754 cm²
1) Prepare a post merger financial position for METRO using the pooling of interest method.
Answer:
Metro and Medec
METRO
Post-merger Financial Position, using the pooling of interest method:
Pre-merger Financial Positions:
Metro (RM ‘000)
Assets
Current assets 120
Fixed assets 830
Total assets 950
Liabilities and Equities
Current liabilities 40
Long term debt 200
Common stock (RM1 par) 480
Capital surplus 120
Retained earnings 110
Total liabilities and equity 950
Earnings available to
common stockholders 230
Common Dividends 150
Addition to Retained Earnings 80
Step-by-step explanation:
Pre-merger Financial Positions:
Metro (RM ‘000) Medec(RM ‘000)
Assets
Current assets 50 70
Fixed assets 650 180
Total assets 700 250
Liabilities and Equities
Current liabilities 30 10
Long term debt 140 60
Common stock (RM1 par) 400 80
Capital surplus 50 70
Retained earnings 80 30
Total liabilities and equity 700 250
Earnings available to
common stockholders 100 130
Common Dividends 50 100
Addition to Retained Earnings 50 30
Exchange ratio = 1:2
