Answer:
The probability of selecting a person which is self-employed but not married equals 1/8.
Step-by-step explanation:
Here, the given survey says:
Total number of people surveyed = 248
Number of people married = 156
The number of people are self employed = 70
Now, 25% of people who are married are SELF EMPLOYED.
Now, calculating 25% of 156 , we get:
[tex]\frac{25}{100} \times 156 = 39[/tex]
⇒ out of total 156 married people, 39 are self employed.
So, number of self employed people but not married
= Self employed people - Self employed people PLUS married
= 70 - 39 = 31.
So, the probability that the person selected will be self-employed but not married = [tex]\frac{\textrm{The total number of people self-employed but not married}}{\textrm{Total Number of people}}[/tex] = [tex]\frac{31}{248} = \frac{1}{8}[/tex]
Hence The probability of selecting a person which is self-employed but not married equals 1/8.
To anticipate the dip and hump in the road, the driver of a car applies her brakes to produce a uniform deceleration. Her speed is 100 km/h at the bottom A of the dip and 50 km/h at the top C of the hump, which is 120 m along the road from A. If the passengers experience a total acceleration of 3 m/s2 at A and if the radius of curvature of the hump at C is 150 m, calculate the radius of curvature rho at A.
Answer:
Therefore the radius of curvature at A is 432.03 m.
Step-by-step explanation:
Radius of curvature : If an object moves in curvilinear motion, then any point of the motion, the radius of circular arc path which best approximates the curve at that point is called radius of curvature.
Radius of curvature =[tex]\rho = \frac{V^2_p}{a}[/tex]
[tex]V_p[/tex]= velocity
a = acceleration perpendicular to velocity.
Velocity at the point A = [tex]V_A= 100 \ km/h[/tex] [tex]=\frac{100 \ km}{1 \ h}= \frac{100\times 1000 \ m}{3600 \ s}=\frac{250}{9}[/tex] m/s
Velocity at the point C [tex]=V_C=50 \ km/ h=\frac{125}{9} \ m/s[/tex]
The distance between A and B is 120 m.
To find the declaration between the point A and C we use the following formula
[tex]V^2_C=V^2_A+2a_ts[/tex]
[tex]\Rightarrow( \frac{125}{9})^2=(\frac{250}9})^2+2a_t.120[/tex]
⇒[tex]a_t[/tex] = -2.41 m/s²
[tex]a_t[/tex]= tangential acceleration
Given the passengers experience a total acceleration of 3 m/s².
Total acceleration= 3 m/s².
[tex]a = \sqrt{a^2_t+a^2_n[/tex]
[tex]\Rightarrow a^2_n= a^2- a^2_t[/tex]
[tex]\Rightarrow a_n=\sqrt{3^2-(-2.41)^2}[/tex]
= 1.786 m/s²
Radius of curvature [tex]\rho_A=\frac{V^2_A}{a_n}[/tex]
[tex]=\frac{(\frac{250}{9})^2}{1.786}[/tex]
= 432.03 m
Therefore the radius of curvature at A is 432.03 m.
Why is the law of cosines a stronger statement than the pythagorean theorem?
Answer:
Answer in explanation
Step-by-step explanation:
The two laws are mathematical laws which are used in navigating problems which involves triangles. While the Pythagorean theorem is used primarily and exclusively for right angled triangle, the cosine rule is used for any type of triangle.
So, why is the cosine rule a stronger statement? The reason is not far fetched. As said earlier, the cosine rule can be used to resolve any triangle type while the Pythagorean theorem only works for right angled triangle. In fact, we can say the Pythagorean theorem is a special case of cosine rule. The reason why the expression is different is that, for the expression, cos 90 is zero, which thus makes our expression bend towards the Pythagorean expression view.
The explanation regarding the law of cosines is the stronger statement if compared with the Pythagorean theorem is explained below.
Difference between the law of cosines be the stronger statement if compared with the Pythagorean theorem:The Pythagorean theorem is used when there is the right-angled triangle, while on the other hand, the cosine rule is used for any type of triangle. Here the Pythagorean theorem should be considered for the special case of cosine rule. Due to this the cosine law should be stronger if we compared it with the Pythagorean theorem.
Learn more about cosine here;https://brainly.com/question/16299322
Select the correct answer. Solve -9 2/7 -(-10 3/7) . A. -1 1/7 B. 1 1/7 C. 19 1/7 D. 19 5/7
Answer:
B. 1 1/7
Step-by-step explanation:
-9 2/7-(-10 3/7)
=-9 2/7+10 3/7
=1 1/7
Therefore, B. 1 1/7
Answer:
The answer is B
Step-by-step explanation:
B. 1 1/7
A scientist measured the exact distance between two points on a map and came up with the following number: 0.04000 km.
Which digits are the significant figures in this measurement?
Explain your answer.
Answer:
The first zero after decimal point and 4 only
Step-by-step explanation:
Despite having 5 decimal points, the rules of significant figures dictate that unless there is a digit other than zero after, the only significant numbers are those that come before zero. For this case, the significant digits are only 0.04 but if it was 0.0400005 then all the other zeros would have also be considered significant.
One number is 20 times another number. The product of the two numbers is 180. Write an equation and use it to find all pairs of numbers that satisfy the
Answer: the Smaller number is 3
The larger number is 60
Step-by-step explanation:
Let x represent the smaller of the numbers.
Let y represent the larger number.
One number is 20 times another number. This means that
y = 20x
The product of the two numbers is 180. This means that
xy = 180- - - - - - - - - -1
Substituting y = 2x into equation 1, it becomes.
x × 20x = 180
20x² = 180
x² = 180/20 = 9
x = √9
x = 3
y = 20x = 20 × 3
y = 60
Look at the proof. Name the postulate you would use to prove the two triangles are congruent.
A. AAA Postulate
B. SSS Postulate SAS
C. SAS Postulate
Answer:
Option C, SAS Postulate
Step-by-step explanation:
I think that it is option C because it does not give you 3 angles or 3 sides, it gives you 2 angles and 1 side.
Answer: Option C, SAS Postulate
PLZ HELP WILL MARK BRAINLIEST
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (3, 2) and point (5, 4) rounded to the nearest tenth?
5.3 units
1 unit
10 units
2.8 units
Answer:
2.8 units
You should get 2√(2) or √(8) which is less than 3 and greater than 2.
Answer: 2.8 units
Step-by-step explanation:
The formula for determining the distance between two points on a straight line is expressed as
Distance = √(x2 - x1)² + (y2 - y1)²
Where
x2 represents final value of x on the horizontal axis
x1 represents initial value of x on the horizontal axis.
y2 represents final value of y on the vertical axis.
y1 represents initial value of y on the vertical axis.
From the given points
x2 = 5
x1 = 3
y2 = 4
y1 = 2
Therefore,
Distance = √(5 - 3)² + (4 - 2)²
Distance = √2² + 2² = √4 + 4 = √8
Distance = 2.8 units
Jerry manages a local car dealership. At the beginning of the month, his lot had m vehicles. During the month his salesman sold n vehicles, and he purchased p vehicles more. How many vehicles did the dealership have at the end of the month?
Answer:
m+p-n
Step-by-step explanation:
given that Jerry manages a local car dealership. At the beginning of the month, his lot had m vehicles. During the month his salesman sold n vehicles, and he purchased p vehicles more
We are to find the number of vehicles did the dealership have at the end of the month
At the end of the month the dealer would have
no of vehicles at the start of the month- sales of the vehicle in that month+Purchase of vechicles during that month
No of vehicles at the start of the month = m
Purchase during month =p
Total vehicles including purchase = m+p
LESS: Vehicles sold in the month = n
No of vehicles at the end = m+p-n
Dont skip plzzzzzzzzzzzzzzzzzzzzzzzz
Answer:
B
Step-by-step explanation:
The slope is rise over run, meaning it is 3/4. The y-intercept is 2, making the equation y = (3/4)x + 2
The caldwells are moving across the country. Mr Caldwell leaves 3 hours before Mrs Caldwell. If he averages 45 mph and she averages 65 mph, how many hours will it take Mrs Caldwell to catch mr. Caldwell
Mrs. Caldwell will travel 135 miles at an additional 20 mph to catch up to Mr. Caldwell. Therefore, it will take Mrs. Caldwell 6.75 hours to catch up to Mr. Caldwell.
Explanation:This is a rate time distance problem in mathematics, typically learned in middle school. To calculate how long it will take Mrs. Caldwell to catch up with Mr. Caldwell, we need to compare the distance traveled by each person in the same time. Because rate equals distance over time (r=d/t), we know that the distance each person traveled is rate x time.
Mr. Caldwell left 3 hours before Mrs. Caldwell, so he traveled at 45 mph for 3 hours, or 135 miles. Once Mrs. Caldwell leaves, she needs to cover these 135 miles at a faster speed to catch up. Her speed is 20 mph greater than Mr. Caldwell’s. We divide the distance that Mr. Caldwell has covered (135 miles) by the difference in their speeds (20 mph) to find it will take Mrs. Caldwell 6.75 hours to catch up to him.
Learn more about Rate Time Distance here:https://brainly.com/question/35683374
#SPJ3
The vertex of this parabola is at (4, -3). Which of the following could be its equation?
A.x = -3(y + 4)2 - 3
B.x = -3(y - 4)2 - 3
C.x = -3(y + 3)2 + 4
D.x = -3(y - 3)2 + 4
Answer:
B) x=-3(y+3)^2+4
Step-by-step explanation:
Plug quadratic in for proof
Answer:
The answer to your question is Letter C
Step-by-step explanation:
Data
Vertex (4, -3)
Process
From the image, we notice that it is a horizontal parabola that opens to the left.
So, it formula must be (y - k)² = 4p(x - h)
-Substitute the vertex
(y + 3)² = 4p(x - 4)
Consider 4p = 1
(y + 3)² = x - 4
Solve for x
x = (y + 3)² + 4
Solution
Letter C
sin= 5/13, and cos b= 3/5, evaluate cos(a-b).
cos (a - b) is 56/65
Step-by-step explanation:
Step 1:Given sin a = 5/13, find cos a.
sin a = opposite side/hypotenuse = 5/13
The adjacent side can be found using Pythagoras Theorem.
Hypotenuse² = Opposite Side² + Adjacent Side²
⇒ Adjacent side² = Hypotenuse² - Opposite Side²
= 13² - 5² = 169 - 25 = 144
∴ Adjacent Side = 12
⇒ cos a = adjacent side/hypotenuse = 12/13
Step 2:Given cos b = 3/5, find sin b.
cos b = adjacent side/hypotenuse = 3/5
The opposite side can be found using Pythagoras Theorem.
Hypotenuse² = Opposite Side² + Adjacent Side²
⇒ Opposite side² = Hypotenuse² - Adjacent Side²
= 5² - 3² = 25 - 9 = 16
∴ Opposite Side = 4
⇒ sin b = opposite side/hypotenuse = 4/5
Step 3:Find cos(a - b).
cos(a - b) = cos a cos b + sin a sin b
= 12/13 × 3/5 + 5/13 × 4/5
= 36/65 + 20/65 = 56/65
What do you know about the solution(s) to the system of equations?
A. There is no solution.
B. The solution is (2,0).
C. The solution is (0,−1).
D. There are infinitely many solutions.
Answer:
A because the linesnever cross.
Step-by-step explanation:
Answer:
There is no solution
Step-by-step explanation:
PLZ HELPPPPPPPPPPPPPPPP
A factory received a shipment of 38 sprockets, and the vendor who sold the items knows there are 5 sprockets in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the sprockets in the sample are defective, he will refuse the shipment.
a) If a sample of 5 sockets is selected, find the probabilty that all in the sample are defective.
b) If a sample of 5 sprockets is selected, find the probability that none in the sample are defective.
Answer:
a) 0.00019923%
b) 47.28%
Step-by-step explanation:
a) To find the probability of all sockets in the sample being defective, we can do the following:
The first socket will be in a group where 5 of the 38 sockets are defective, so the probability is 5/38
The second socket will be in a group where 4 of the 37 sockets are defective, as the first one picked is already defective, so the probability is 4/37
Expanding this, we have that the probability of having all 5 sockets defective is: (5/38)*(4/37)*(3/36)*(2/35)*(1/34) = 0.0000019923 = 0.00019923%
b) Following the same logic of (a), the first socket have a chance of 33/38 of not being defective, as we will pick it from a group where 33 of the 38 sockets are not defective. The second socket will have a chance of 32/37, and so on.
The probability will be (33/38)*(32/37)*(31/36)*(30/35)*(29/34) = 0.4728 = 47.28%
A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec2 is given by the linear graph below for the time interval [0, 30]. At t = 0, the velocity of the car is 0 and its position is 10.
What is the total distance the car travels in this 30 second interval? Your must show your work but you may use your calculator to evaluate. Give 3 decimal places in your answer and include units.
Im not really sure how to go about this? Would I use the trapezoidal rule i dont know please help.
Answer:
666.667 feet
Step-by-step explanation:
Slope = -1
Intercept = 10
y = -t + 10
y is the acceleration
Integrate y fornv
v = -t²/2 + 10t + c
At t=0, v=0 so c = 0
v = -t²/2 + 10t
Turns when v = 0,
-t²/2 + 10t = 0
t = 0, 20
Integrate v for s
s = -t³/6 + 5t² + c
At t = 0, s = 10
10 = c
s = -t³/6 + 5t² + 10
s at t=30,
-(30³)/6 + 5(30)² + 10
= 10m
(Back to starting point)
At t = 20,
Displacement in
-(20³)/6 + 5(20)² + 10
= 343.333
Total distance = 2(343.333-10)
= 666.6667
The total distance the car travels in this 30 second interval is 1333.34 units
From the graph, we have the following points
(0, 10) and (10, 0).
Start by calculating the slope (m) of the graph
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{0 - 10}{10-0}[/tex]
[tex]m =- \frac{10}{10}[/tex]
[tex]m =- 1[/tex]
The equation is then calculated as:
[tex]y = m(x -x_1) + y_1[/tex]
This gives
[tex]y = -1(x -0) + 10[/tex]
[tex]y = -1x+ 10[/tex]
[tex]y = -x+ 10[/tex]
The above equation represents the acceleration (y) as a function of time (x).
Integrate to get the velocity (v)
[tex]v = -\frac{x\²}{2} + 10x + c[/tex]
From the question, we have:
The velocity (v) of the car is 0, when the time (x) is 0.
So, we have:
[tex]0 = -\frac{0\²}{2} + 10(0) + c[/tex]
This gives
[tex]c = 0[/tex]
So, the equation becomes
[tex]v = -\frac{x\²}{2} + 10x + 0[/tex]
[tex]v = -\frac{x\²}{2} + 10x[/tex]
Set v = 0.
So, we have:
[tex]-\frac{x\²}{2} + 10x = 0[/tex]
Multiply through by -2
[tex]x^2 -20x = 0[/tex]
Factorize
[tex]x(x -20) = 0[/tex]
Split
[tex]x = 0\ or\ x -20 = 0[/tex]
Solve for x
[tex]x = 0[/tex] or [tex]x = 20[/tex]
Integrate velocity (v) to get the displacement (d)
[tex]v = -\frac{x\²}{2} + 10x[/tex]
[tex]d = -\frac{t\³}{6} + 5t\² + c[/tex]
From the question, we have:
The position (d) of the car is 10, when the time (x) is 0.
So, we have:
[tex]-\frac{(0)\³}{6} + 5(0)\² + c = 10[/tex]
[tex]c = 10[/tex]
So, the equation becomes
[tex]d = -\frac{t\³}{6} + 5t\² + 10[/tex]
The position at 30 seconds is:
[tex]d = -\frac{(30)\³}{6} + 5(30)\² + 10[/tex]
[tex]d = 10[/tex]
The position at 20 seconds is:
[tex]d = -\frac{(20)\³}{6} + 5(20)\² + 10[/tex]
[tex]d = 676.667[/tex]
The total distance is then calculated as:
[tex]Total = 2 \times (d_2 -d_1)[/tex]
This gives
[tex]Total = 2 \times (676.667 -10)[/tex]
[tex]Total = 2 \times 666.667[/tex]
[tex]Total = 1333.34[/tex]
Hence, the total distance is 1333.34 units
Read more about distance at:
https://brainly.com/question/2239252
(1 point) A rock is thrown into a still pond and causes a circular ripple. If the radius of the ripple is increasing at a rate of 4 feet per second, how fast is the circumference changing when the radius is 18 feet?
Answer:
8pi feet per second
Or, 25.1 feet per second (3 sf)
Step-by-step explanation:
C = 2pi×r
dC/dr = 2pi
dC/dt = dC/dr × dr/dt
= 2pi × 4 = 8pi feet per second
dC/dt = 25.1327412287
y = x + 2y = -2x + 2y = -3x + 2y = -5x + 2y = -
3
2
x + 2y = -
5
2
x + 2y = -x + 2y = 2x + 2y = 5x + 2y =
5
2
x + 2
0
Answer:
i need more context
Step-by-step explanation:
A pure acid measuring x liters is added to 300 liters of a 20% acidic solution. The concentration of acid, f(x), in the new substance is equal to the liters of pure acid divided by the liters of the new substance, or . Which statement describes the meaning of the horizontal asymptote? The greater the amount of acid added to the new substance, the more rapid the increase in acid concentration. The greater the amount of acid added to the new substance, the closer the acid concentration is to one-fifth. As more pure acid is added, the concentration of acid approaches 0. As more pure acid is added, the concentration of acid approaches 1.
Answer:
the answer is d
Step-by-step explanation:
Trevor Once to buy a car that cost 23600 he has 5000 for down payment how much more will Trevor O the car right solve and create an equation for his situation define the variable
Answer:
5000 + x = 23600
Step-by-step explanation:
a car that cost = 23600
down payment = 5000
So he needs to pay: 23600 - 5000 = 18600 more to get the car
Let x represent the amount he needs to pay more, an equation for his situation:
5000 + x = 23600
Tara bought Three boxes of dog treats with 40 truth in each box two boxes of cat treats with 20 trees in each box simplify the expression below to find the total number of trees are bought
Answer:
Tara bought a total of 160 treats.
Step-by-step explanation:
We are given the following in the question:
Number of boxes of dog treats = 3
Number of treats in each dog box = 40
Total number of treats in dog box =
[tex]40 \times 3 = 120[/tex]
Number of boxes of cat treats = 2
Number of treats in each cat box = 20
Total number of treats in cat box =
[tex]20\times 2 = 40[/tex]
Total number of treats Tara brought =
Total number of treats in dog box + Total number of treats in cat box
[tex](40\times 3)+(20\times 2)\\= 120 + 40\\=160[/tex]
Thus, Tara bought a total of 160 treats.
When I count as a principal of $1000 and earns 4% simple interest per year and other account as a principal $1000 and earns 4% interest compounded annually which account has the greater balance at the end of four years
Answer: the account that earned compound interest has the greater balance at the end of four years.
Step-by-step explanation:
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the amount invested.
P represents the principal or amount invested.
R represents interest rate
T represents the duration of the investment in years.
From the information given,
P = 1000
R = 4%
T = 4 years
I = (1000 × 4 × 4)/100 = 160
Total amount earned is
1000 + 160 = $1160
The formula for determining compound interest is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 1000
r = 4% = 4/100 = 0.04
n = 1 because it was compounded once in a year.
t = 4 years
Therefore,.
A = 1000(1+0.04/1)^1 × 4
A = 1000(1.04)^4
A = $1170
A scoop of ice cream has a 3 inch radius. How tall should the ice cream cone of the same radius be in order to contain all of the ice cream inside the cone?
Answer:
12cm
Step-by-step explanation:
The scoop of Ice Cream is in the shape of a circular solid which is a Sphere.
For the ice cream to fit into the cone, the volume of the cone must be equal to that of the sphere.
Radius of the Sphere=3cm
Volume of a Sphere = [tex]\frac{4}{3}\pi r^3[/tex]
Volume of a Cone=[tex]\frac{1}{3}\pi r^2h[/tex]
[tex]\frac{1}{3}\pi X 3^2h=\frac{4}{3}\pi X 3^3\\\frac{1}{3}h=\frac{4}{3} X 3\\\frac{1}{3}h=4\\h=4 X 3=12cm[/tex]
The Cone of same radius must be 12cm tall.
100 pyramid shaped chocolate candies with a square base of 12 mm size and height of 15 mm are melted in a cylinder coil pot if the part has a radius of 75 mm what is the height of the melted candies in the pot.
Answer: the height of the melted candies in the pot is 12.2 mm
Step-by-step explanation:
The formula for determining the volume of a square base pyramid is expressed as
Volume = area of base × height
Area of the square base = 12² = 144 mm²
Volume of each pyramid = 15 × 144 = 2160 mm³
The volume of 100 pyramid shaped chocolate candies is
2160 × 100 = 216000 mm³
The formula for determining the volume of a cylinder is expressed as
Volume = πr²h
Since the pyramids was melted in the cylindrical pot whose radius is 75 mm, it means that
216000 = 3.14 × 75² × h
17662.5h = 216000
h = 216000/17662.5
h = 12.2 mm
Answer:
The height of the melted candies in the pot is 4.07mm
Step-by-step explanation:
H= 100*1/3(12)^2(15)/π(75)^2=64/5π=4.07
For a given data set, the equation of For a given data set, the equation of the least squares regression line will always pass throughthe least squares regression line will always pass through
For a given data set, the equation of the least squares regression line will always pass through the point [tex]\((\bar{x}, \bar{y})\),[/tex] where [tex]\(\bar{x}\)[/tex] is the mean of the x-values and[tex]\(\bar{y}\)[/tex] is the mean of the y-values.
Explanation:The least squares regression line minimizes the sum of squared differences between the observed y-values and the values predicted by the line. The equation of the line is given byy = mx + b, where m is the slope and bis the y-intercept. The slopem and y-intercept b are determined by formulas involving the means[tex](\(\bar{x}\)[/tex] and [tex]\(\bar{y}\))[/tex]and other statistical measures from the data set.
The specific formulas for the least squares regression line are:
[tex]\[ m = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{\sum_{i=1}^{n} (x_i - \bar{x})^2} \]\[ b = \bar{y} - m\bar{x} \][/tex]
It can be observed from the formulas that when [tex]\(x = \bar{x}\)[/tex], the corresponding y value is[tex]\(\bar{y}\)[/tex]. Therefore, the least squares regression line passes through the point[tex]\((\bar{x}, \bar{y})\)[/tex]. This point represents the centroid of the data set and ensures that the line adequately represents the overall trend of the data.
Question:
It seems there might be some repetition or an incomplete question in your request. Could you please provide more details or clarify your question so that I can assist you accurately? If you have a specific question related to the least squares regression line or any other topic, feel free to provide more context, and I'll do my best to help you.
A right cylindrical solid is cut in half to form the figure shown. If the length is 20 cm and the diameter is 8 cm, what is the surface area?
(80π + 160) cm2
(96π + 160) cm2
320π cm2
(320π + 160) cm2
Answer:
(96π + 160) cm2
Step-by-step explanation:
HELP HOW DO I FIND THE B VALUE OF THIS
Answer:
b = [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
period = [tex]\frac{2\pi }{b}[/tex], that is
b = [tex]\frac{2\pi }{period}[/tex] = [tex]\frac{2\pi }{\frac{3\pi }{4} }[/tex] = 2π × [tex]\frac{4}{3\pi }[/tex] = [tex]\frac{8}{3}[/tex]
Answer:
f(x) = 4cos(8/3)x - 3.
The missing space is 8/3.
Step-by-step explanation:
The general form is f(x) = Acosfx + B where A = the amplitude, f = frequency and B is the vertical shift..
Here A is given as 4, B is - 3 and the frequency f = 2 π / period =
2π / (3π/4)
= 8/3.
So the answer is f(x) = 4cos(8/3)x - 3.
At 9:00, Paula has x cups of food in a container. Pamula pours 2 1/2 cups of food into the container. Then she removes 3/4 cups of food to feed her dog. Now there are 5 1/4 of food in the container. What is the equation?
Answer:
The equation representing the scenario is [tex]x+\frac{5}{4}-\frac{3}{4} = \frac{21}{4}[/tex].
Step-by-step explanation:
Given:
Amount of food in the container = [tex]x \ cups[/tex]
Amount of food added in the container = [tex]2\frac12\ cups[/tex]
We will now convert the mixed fraction into Improper fraction by Multiplying the whole number part by the fraction's denominator and then add that to the numerator and then write the result on top of the denominator.
[tex]2\frac12\ cups[/tex] can be rewritten as [tex]\frac{5}{4}\ cups[/tex]
Amount of food added in the container = [tex]\frac{5}{4}\ cups[/tex]
Amount of food removed from container to feed dog = [tex]\frac34 \ cups[/tex]
Amount of food remaining = [tex]5\frac{1}{4} \ cups[/tex]
[tex]5\frac{1}{4} \ cups[/tex] can be Rewritten as = [tex]\frac{21}{4}\ cups[/tex]
Amount of food remaining = [tex]\frac{21}{4}\ cups[/tex]
We need to write the equation for above scenario.
Solution:
Now we can say that;
Amount of food remaining is equal to Amount of food in the container plus Amount of food added in the container minus Amount of food removed from container to feed dog.
framing in equation form we get;
[tex]x+\frac{5}{4}-\frac{3}{4} = \frac{21}{4}[/tex]
Hence the equation representing the scenario is [tex]x+\frac{5}{4}-\frac{3}{4} = \frac{21}{4}[/tex].
In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?
A) 5
B) 4
C) 3
D) 2
E) 0
Answer: Option 'D' is true.
Step-by-step explanation:
Since we have given that
Number of points are 7,5,3, and 2 each.
Product of the point values of the removed beads = 147000
So, the possible way is given by
[tex]2^3\times 3\times 5^3\times 7^2=147000[/tex]
Since no other beads is a multiple of 7.
So, there must be two red beads removed.
Hence, Option 'D' is true.
In order to develop a more appealing cheeseburger, a franchise uses taste tests with 15 different buns, 8 different cheeses, 3 types of lettuce, and 4 types of tomatoes. If the taste tests were done at one restaurant by one tester who takes 10 minutes to eat each cheeseburger, approximately how long would it take the tester to eat all possible cheeseburgers?
Answer:
There would be
13 x 8 x 4 x 3 = 3,276 different cheeseburger combinations
If the taste tester takes 10 minutes to eat a cheeseburger, then it would take him
3276 x 10 = 32760 minutes
Eating round the clock, it would take him
32760 / 60 = 546 hours
546 / 24 = 22 days 18 hours
Now these are the numbers I'm seeing
1313 buns
88 cheese
44 lettuces
33 tomatoes
There would be
1313 x 88 x 44 x 33 = 167,769,888 different cheeseburger combinations
If the taste tester takes 10 minutes to eat a cheeseburger, then it would take him
167769888 x 10 = 1,677,698,880 minutes
1677698880 / 60 = 27,961,647 hours
27961647 / 24 = 1,165,068.62 days
1165068.62 / 365 = 3,191.97 years
Step-by-step explanation: