The cost of the cereal if the grocery store buys 250 boxes is $475
Cost functionsFunctions are written in terms of variables. If the cost function that represents the cereal is given as C(n), the equivalent expression if the grocery store buys 250 boxes is 1.9n
Substitute n = 250 into the function to have:
C(250) = 1.9(250)
C(250) = $475
Hence the cost of the cereal if the grocery store buys 250 boxes is $475
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A rectangle's length is three times as long as it is wide. Which expression represents the change in area if the width of the rectangle is increased by 1?
1. 3x^2
2. 3x
3. 3x^2+3x
4. the area increases by 3
Step-by-step explanation:
Let's say the rectangle's width is equal to y. We know that the length is three times the width, so the length = 3 * y. We also know that the area for a rectangle is equal to length * width, so the area, z, is equal to
(3*y) * y = z
3 * y² = z
Now, let's increase the width of the rectangle by 1. We can replace y with y+1 (as y+1 is 1 greater than y), and 3 * y with 3 * (y+1) to get
3*(y+1) * (y+1) = new area
(3y+3)*(y+1) = new area
3y²+3y +3 y + 3 = new area
3y² + 6y + 3 = new area
The difference in area is equal to the new area subtracted by the old area, or
3y²+6y+3 - 3y² = 6y +3. The variable for x is not given, so if x = (2y+1), the answer would be the second choice. However, solely using the information given, it is impossible to determine a solution outside of saying that it is not option 4, as 6y + 3 ≠ 3
verify that whether -2 and 3 are zeroes of the polynomial x^2-x=6
PLEASE HELP
Answer:
Both give remainder 0 for the polynomial
Step-by-step explanation:
p(-2) = (-2)² - (-2) - 6
= 6 - 6 = 0
p(3) = (3)² - 3 - 6
= 9 - 9 = 0
A town has a current population of 4,000. The population increased 4 percent per year for the past four years, Emergency response professionals
make up 3 percent of the town's population.
Part A
Write a function that represents the population (p) of the town in terms of the number of years (1) for the last four years.
Answer:
p=c(1+r)^t so the population will be 4679.43424 or rounded to 4679
Step-by-step explanation:
p=c(1+r)^t
p=4,000(1+.04)^t
p=4,000(1.04)^t
p=4,000(1.04)^4
p=4679.43424
p= the population you are solving for
c= the initial amount of the population
(1+r)= the rate of change
t= the period of time
The exponential equation that represents the population of the town in terms of the number of years : [tex]p=4000 (1+0.4)^{t}[/tex]
What is an exponential equation?An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.
It is similar to the amount received after investing a certain amount compounded annually.
Given,
Initial population = 4000
Rate of increase = 4%
Let current population be p.
Let number of years passed be t.
The exponential equation will be: [tex]p=4000 (1+0.4)^{t}[/tex]
(The population of the town has grown exponentially. This means that:
Initial population = 4000
Population in year I = 4000 + 4% of 4000 = 4000(1 + 0.4)
Population in year II = 4000 + 4% of 4000(1 + 0.4) = 4000(1 + 0.4)(1+0.4)
and this goes on.)
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In the figure, ∆ABD ≅ ∆CBD by Angle-Side-Angle (ASA). Which segments are congruent by CPCTC?
Answer:
[tex]\angle ADB \cong \angle CDB[/tex]
[tex]\angle DBA \cong \angle DBC[/tex]
[tex]BD = BD[/tex]
Step-by-step explanation:
Given
[tex]\triangle ABD \cong \triangle CBD[/tex]
Required
The congruent segments by CPCTC
From the question, we have:
[tex]\angle ADB \cong \angle CDB[/tex] --- given
[tex]\angle DBA \cong \angle DBC[/tex] --- given
Both triangles share a common side (length BD);
So, we have:
[tex]BD = BD[/tex]
Hence, the congruent segments are:
[tex]\angle ADB \cong \angle CDB[/tex]
[tex]\angle DBA \cong \angle DBC[/tex]
[tex]BD = BD[/tex]
In how many ways can a sample of 6 keyboards be selected so that exactly two have an electrical defect
Answer:
15ways
Step-by-step explanation:
This is a combination question since combination has to do with selection. Hence the number of ways sample of 6 keyboards can be selected so that exactly two have an electrical defect is expressed as;
6C2 = 6!/(6-2)!2!
6C2 = 6!/4!2!
6C2 = 6×5×4!/4!×2
6C2 = 6×5/2
6C2 = 30/2
6C2 = 15
Hence this can be done in 15ways
a mean equal to 5 cm. A simple random sample of wrist breadths of 40 women has a mean of 5.07
cm. The population standard deviation is 0.33 cm. Find the value of the test statistic?
Answer:
The value of the test statistic is [tex]z = 1.34[/tex]
Step-by-step explanation:
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Test if the mean is equal to 5:
This means that the null hypothesis is [tex]\mu = 5[/tex]
A simple random sample of wrist breadths of 40 women has a mean of 5.07 cm. The population standard deviation is 0.33 cm.
This means that [tex]n = 40, X = 5.07, \sigma = 0.33[/tex]
Find the value of the test statistic?
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{5.07 - 5}{\frac{0.33}{\sqrt{40}}}[/tex]
[tex]z = 1.34[/tex]
The value of the test statistic is [tex]z = 1.34[/tex]
In golf, scores are often written in relationship to par, the average score for a round at a certain course. Write an integer to represent a score that is 7 under par.
Answer:
-7
Step-by-step explanation:
If it is 7 below (a key word, which you can connect to 'negative'), then you just write it as -7.
the sum of the square of the number and a second number is 42
Step-by-step explanation:
x+x squared =42. The square of the number is the number square. By my incredibly accurate guess and check strategy (works most of the time )6*6 = 36+6=42
A rectangular field 50 meters in width and 120 meters in length is divided into two fields by a diagonal line. What is the length of fence (in meters) required to enclosed one of these fields?
A-130
B-170
C-180
D-200
E-300
Answer:
E. 300
Step-by-step explanation:
A rectangle split in half diagonally yields 2 right triangles.
((For this problem, you are probably supposed to use the pythagorean theorem to find the diagonal length, and then calculate perimeter (length of fence around triangular field). In other words:
(sqrt( (50m)^2 + (120m)^2 )) + 50m + 120m)
))
By definition, the hypotenuse (diagonal) is the longest side.
This means that it must be longer than 120m.
If you add the 2 sides (50m + 120m), you get 170m.
Since the third side has to be longer than 120m, the answer _must_ be over 290m (170m + 120m).
300m is the only answer that fits.
For the expression x-5, what would the value be if x=18?
Answer:
13
Step-by-step explanation:
Answer:
if x is 18 replace 18 where x is in the question so, it will be 18-5 = 13
Determine if each proportion on the left is true or false
9514 1404 393
Answer:
FalseTrueTrueTrueStep-by-step explanation:
An easy way to tell if the equation is true is to multiply it by the product of the denominators (cross multiply).
7×7 ≠ 12×4 . . . . proportion is False
9×8 = 36×2 . . . . proportion is True
8×9 = 24×3 . . . . proportion is True
5×104 = 8×65 . . . . proportion is True
A computer disk that once sold for $2.25 now sells for 25% less. How much does the computer.
Answer:
$ 1.6875 or $1.69 or $1.70
determine the general solution of cos2X -7cosX -3=0
Answer:
x=2pi/3 +2pi n, 4pi/3 +2pi n for all integar of n.
Step-by-step explanation:
Can someone please help?
Find the value of x for the right triangle.
Answer:
5
Step-by-step explanation:
cos60° = x / 10
10cos60° = x
10cos60° = 5
to
W
3 62 Average Speed During the first part of a 6-hour
trip, you travel 240 miles at an average speed of r
miles per hour. For the next 72 miles of the trip, you
?
increase your speed by 10 miles per hour. What were
your two average speeds?
nd
69
How to solve
Answer:
40 and 10.33
Step-by-step explanation:
240÷6=40.. 72-10=62 62÷6=10.33
An assignment is worth 300 points for each day the assignment is late the professor deduct 10 points from the assignment and grade
Answer:
Eh whats the question? it takes 30 days for the assignemnt to be zero if that is the question.
Step-by-step explanation:
Answer:
points = 300 - 10 L
x = 300 - 10Y
x = points, Y = days late
Step-by-step explanation:
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
find the slope and y-intercept of line 3x +y -9=0
Answer:
x-intercept(s):(3,0)
y-intercept(s):(0,9)
Step-by-step explanation:
Lorena and Julio purchased a home for $205,950. Their loan amount was $164,760, and the assessed value is now $200,500. Their tax rate is 1.5%. How much will their monthly taxes be?
Answer:
Monthly taxes = $250.63 (Approx.)
Step-by-step explanation:
Given:
Amount of purchase = $205,950
Loan amount = $164,760
Assessed value = $200,500
Tax rate is 1.5%
Find:
Monthly taxes
Computation:
Tax always calculated on Assessed value
Annual tax amount = 200,500 x 1.5%
Annual tax amount = 3,007.5
Monthly taxes = Annual tax amount / 12
Monthly taxes = 3,007.5 / 12
Monthly taxes = 250.625
Monthly taxes = $250.63 (Approx.)
In ABC, if CB AC≅ , m∠A = 3x + 18, m∠B = 7x – 58, and m∠C = 2x – 8, find x and the measure of each angle.
9514 1404 393
Answer:
x = 19
A = 30°
B = C = 75°
Step-by-step explanation:
In an isosceles triangle, the angles opposite the congruent sides have the same measures.
A = B
3x +18 = 7x -58
76 = 4x . . . . . . . . add 58-4x
19 = x . . . . . . . . . divide by 4
Then the equal angles measure ...
A = B = 3(19) +18 = 75
C = 2(19) -8 = 30
Angles A, B, C measure 75°, 75°, 30°, respectively.
_____
Alternate solution
The sum of angles in a triangle is 180°, so you could write ...
(3x +18) +(7x -58) +(2x -8) = 180
12x = 228 . . . . . add 48
x = 19 . . . . . divide by 12
She uses a scale of 1 centimeter to 6 inches
the scale drawing of the front face is
Answer:
change inches into centimeter and then divide it
hope this help
An airplane can travel 350 mph in still air. If it travels 1995 miles with the wind
in the same length of time it travels 1505 miles against the wind, what is the speed of the wind?
Answer:
49 mph
Step-by-step explanation:
RT=D
T = D/R
[tex]\frac{1995}{(350 + x) } =\frac{1505}{350-x}[/tex]
1995(350-x) = 1505(350+x)
x=49
Use the theoretical method to determine the probability of the outcome or event given below.
The next president of the United States was born on Monday
Answer:
[tex]\frac{1}{7}[/tex] probability that the next president of the United States was born on Monday
Step-by-step explanation:
A theoretical probability is given by the number of desired outcomes divided by the number of total outcomes.
The next president of the United States was born on Monday
Any person, including the next president of the United States, can be born on 7 possible days: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday or Saturday, one of which is Monday.
So
[tex]\frac{1}{7}[/tex] probability that the next president of the United States was born on Monday
At a store sales tax is charged at a rate of 2% on the cost price of an item . the sales tax on a dress which cost $180 is
Answer:
$3.60
Step-by-step explanation:
100% = 180
1% = 180/100 = $1.80
2% = 1%×2 = 1.8×2 = $3.60
Help me with moth of these questions please
Answer:
10. CD + DE = CE
11. BC + CE = BE
Step-by-step explanation:
10. CD and DE lie on a straight line, therefore, CD + DE = CE based on the segment addition postulate.
11. BC and CE lie on a straight line, therefore, BC + CE = BE based on the segment addition postulate.
solve the following by factolisation formula
1. x(2x+1)=0
2.4xsquere-11-3x=0
1.
X = 0
2x + 1 = 0
X = 0
X = - ½ (Because we brought the numbers from one side to the other)
2.
Not sure for number 2.
Can you help please fellow people
Answer:
using 2 below points to draw:
(0, 7)
(3.5, 6)
Step-by-step explanation:
using
Which of the following best describes the data distribution of the histogram below?
A. Symmetric
B. Uniform
C. Bimodal
D. Unimodal
Answer:
D. Unimodal
Step-by-step explanation:
We can immediately tell the data is not symmetrical. That leaves B, C, D. The data of this histogram is also not uniform because the numbers vary- eliminating answer choice B. There are three modes of data distribution; unimodal, multimodal, and bimodal. The one demonstrated here is unimodal because there is one "hump" in the data distribution of the histogram and one mode.
The three modes of data distribution for visual context:
If a line is equation 5 x + 6 Y is equal to 2 k together with the coronavirus access from a triangle of area 135 square unit.find the value of k.
Answer:
hdhdkdbddkdgsjshzcssjsn
PLEASE HELP!!! WILL GIVE BRAINLIEST!!!!!!
Answer:
78.93 yan ats yung sagot hula ko
Answer:
it is 78.93 yun
hope this will help you
