Answer:
290 + 5m = 985
Step-by-step explanation:
Given information:
Initial payment = $290Total payment = $985Extra amount each month = mLength of rental = 5 monthsFrom the given information, we can create the following equation:
Initial payment plus extra amount each month for 5 months equals total payment.
⇒ 290 + 5m = 985
To solve the equation:
Subtract 290 from both sides:
⇒ 290 + 5m - 290 = 985 - 290
⇒ 5m = 695
Divide both sides by 5:
⇒ 5m ÷ 5 = 695 ÷ 5
⇒ m = 139
Therefore, the extra amount George paid each month was $139.
Answer: [tex]\Large\boxed{290+5m=985}[/tex]
Step-by-step explanation:
Given information
Initial cost = $290
Total cost = $985
Number of months = 5 months
Cost each month = ?
Set variable
Let [ m ] be the cost each month
The equation in verble sense
Initial paid + Extra each month = Total cost
Convert verbal equation to mathematical sense
$290 + 5m = $290
Therefore, to find the extra amount paid each month, the equation is [tex]\Large\boxed{290+5m=985}[/tex]
---------------------------------------------------------------------------------------------------------
EXTRA The following will be solving the derived equation, please ignore this part if it is useless for you.
Given equation
290 + 5m = 985
Subtract 290 on both sides
290 + 5m - 290 = 985 - 290
5m = 695
Divide 5 on both sides
5m / 5 = 695 / 5
m = $139
Hope this helps!! :)
Please let me know if you have any questions
In a study of 250,178 cell phone users,it was found that 81 developed cancer of the brain or nervous system. Assuming that cell phones have no effect, there is 0.000412 probability of a person developing cancer of the brain or nervous system. We therefore expect about 104 cases of such cancer in a group of 250,178 people.Estimate the probability of 81 or fewer cases of such cancer in a group of 250,178. What do these results suggest about media reports that all cell phone cause cancer of the brain or nervous system?
P(x≤81)=[tex]P(x\leq 81)\\What do these results suggest about media reports?[/tex]
Using the normal distribution, the probability is given as follows:
P(x≤81) = 0.0158.
Since this probability is very small, less than 0.05, it suggest that the media reports overstated the proportion of cellphone users that developed cancer.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].For this problem, the proportion and the sample size are given by:
p = 0.000412, n = 250178
Hence the mean and the standard deviation for the approximation are given by:
[tex]\mu = np = 250178 \times 0.000412 = 103.1[/tex].[tex]\sigma = \sqrt{np(1-p)} = \sqrt{250178 \times 0.000412 \times (1 - 0.000412)} = 10.15[/tex]The probability that x is of 81 or less than the p-value of Z when X = 81.5, accounting for continuity correction, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{81.5 - 103.1}{10.15}[/tex]
Z = -2.13
Z = -2.13 has a p-value of 0.0158.
Hence:
P(x≤81) = 0.0158.
Since this probability is very small, less than 0.05, it suggest that the media reports overstated the proportion of cellphone users that developed cancer.
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Draw out a two column proof for each problem below. Complete all problems on one page and upload ONE photo of the entire assignment Make sure your file/image is clear (not blurry) and easy to read. Problem 1. Congruent Triangle Proof (10 Points) Given: NQ is the bisector of MNP and NMQ ~ ZNPQ| Prove: A MNQA PNQ 0 Problem 2. Proof Involving CPCTC (14 Points) Given: S is the midpoint of QR QR PS and RSP and QSP are right angles. Prove: PR PQ S 0
Two or more triangles are congruent if on comparison, they have equal lengths of sides, and measure of angles.
Therefore, the required proofs for each question are shown below:
Problem 1:
Congruent triangles are triangles with equal lengths of corresponding sides and measures of internal angles.
Thus,
STATEMENT REASON
1. <NMQ ≅ <NPQ Any point on a perpendicular bisector
makes equal measure of angle with the
two ends of the line segment.
2. NQ ⊥ MP Definition of a line.
3. MQ ≅ PQ Equal segments of a bisected line.
4. MN ≅ PN Any point on a perpendicular bisector
is at the same distance to the
two ends of the line segment.
5. <MNQ ≅ <PNQ Equal measure of the bisected angle.
Problem 2:
A line segment is the shortest distance between two points.
STATEMENTS REASONS
1. m<PSR ≅ m<PSQ A perpendicular bisector is always at a right
angle to the bisected line segment.
2. m<RPS ≅ m<QPS Equal measure of the bisected angle.
3. RS ≅ QS Property of a bisected line segment.
4. PR ≅ PQ Any point on a perpendicular bisector
is at the same distance to the two ends of
the line segment.
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A large high school has 3,000 students.
During a one-week period, 75 students were
selected at random various times of the day.
Each student was asked if he or she had one
or more social media accounts. The survey
found that 3 out of 75 students did not have
any social media accounts. Estimate the
number of students in the entire school who
do not have social media accounts.
Answer:
120 students don't have social media accounts
Step-by-step explanation:
Whether the sample is representative:
Estimate: [tex]\frac{3}{75} (3000)=\frac{9000}{75} =120[/tex]
Hope this helps
A Ferris wheel with a diameter of 10 m and makes one complete revolution every 80
seconds. Assume that at time t = 0, the Ferris Wheel is at its lowest height above
the ground of 2 m. You will develop the equation of a cosine graph that models your
height, in metres, above the ground as you travel on the Ferris Wheel over time, t in
seconds. To do this, answer the following questions.
1. State the amplitude of the graph.
2. State the value of k in the general form y = a cos [k(x - d)] + c.
3. State the value of d.
4. State the value of c.
5. State the cosine equation of the graph.
The cosine equation of the attached graph is; y = 5 cos [( π/40)(x - (π/2))] + 3
How to plot a trigonometric graph?
The given parameters are:
Diameter = 10 m
Thus;
Radius; r = 5 m
Time; t = 80 s
Height above the ground, h = 2 m
The above means that:
Amplitude; A = 5 m
Period, T = 80 s
Minimum = 2 m
The cosine function is represented as:
y = a cos [k(x - d)] + c.
where;
A is amplitude
B is cycles from 0 to 2π
period = 2π/k
d is horizontal shift
c is vertical shift (displacement)
Thus;
2π/k = 80
k = 2π/80 = π/40
Where
c = Amplitude - Minimum
c = 5 - 2
c = 3
Shift to the left by π/2 gives;
d = π/2
Thus, the equation of the cosine graph is;
y = 5 cos [( π/40)(x - (π/2))] + 3
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A scientist is tagging fish in the Allentown Lake. She catches a fish, tags it,and releases it back into the water. The scientist knows the exact number of fish in the lake: 32 bass,14 fluke,10 carp, and 3 bull sharks.
Calculate the probabilities that the scientist will catch:
A. a bass and then a carp
B. two consecutive bull sharks
C. a fluke and then any different type of fish
d. a bass, another bass, and a bull shark
Probability has to do with the possibility that an event may or may not happen.
What is the probability?The term probability has to do with the possibility that an event may or may not happen. The value of probability always ranges from zero to one.
Now;
Total number of fishes = 32 + 14 + 10 + 3 = 59
a) probability of catching a bass and then a carp = 32/59 * 10/59 = 320/3481
b) probability of catching two consecutive bull sharks= 3/59 * 3/59 = 9/3481
c) probability of catching a fluke and then any different type of fish 14/59 * (32/59 + 10/59 + 3/59) = 14/59 * 45/59 = 630/3481
d) probability of catching a bass, another bass, and a bull shark = 32/59 * 32/59 * 3/59 = 3072/205379
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A company that produces dog food claims that its bags contain 11 kg of food. From
prior experimentation, it is known that the weight of the dog food in these bags is normally
distributed with a standard deviation of 0.6 kg. From a random sample of 25 bags, the mean
weight of the dog food was 10.6 kg. We are concerned that the company is exaggerating how
much dog food they put in their bags. Test at the 5% significance level.
By testing the hypothesis we can conclude that the bag does not contain 11 kg of food.
Given mean of 10.6 kg, population standard deviation of 0.6 and sample size of 25.
We are required to find whether the company is right in saying that their bags contain 11 kg of food.
First we have to make hypothesis.
[tex]H_{0}[/tex]:μ≠11
[tex]H_{1}[/tex]:μ=11
We have to use t statistic because the sample size is less than 30.
t=(X-μ)/s/[tex]\sqrt{n}[/tex]
We will use s/[tex]\sqrt{n}[/tex]=0.6 because we have already given population standard deviation of weights.
t=(11-10.6)/0.6
=0.4/0.6
=0.667
Degree of freedom=n-1
=25-1
=24
T critical at 0.05 with degree of freedom 24=2.0639
T critical at 0.05 with degree of freedom is greater than calculated t so we will accept the null hypothesis.It concludes that the bags donot contain 11 kg of food.
Hence by testing the hypothesis we can conclude that the bag does not contain 11 kg of food.
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The letters of "EAGLES" should be evenly spaced across a 70-inch-wide banner, with no margins. Each letter is 10 inches wide. How many inches (x) should exist between each pair of letters
Answer:
2 Inches or ~1.43 Inches
Step-by-step explanation:
2 Inches if it's not including the spacing before the first "E" and after the "S", ~1.43 Inches if it's including the spacing.
You would get 2 Inches since if each letter is 10 inches (total 6 letters), that would be 60 inches. There are 5 total spaces in between all the letters. 70 Inches(Banner size) - 60 Inches (total letter size) = 10 Inches, divided equally within the 5 spaces. That would equal 2 :)
You also get ~1.43 Inches by doing the same process as the one shown above^ (that is if you're including the spacing before and after the word)
:)
Copy the problem, mark the givens in the diagram and write a statement/reason proof
Answer:
Step-by-step explanation:
<E = <T Given
M is the midpoint of TE Given
TM = ME Definition of a midpoint
<TMI = <RME Property of Vertically Opposite Angles
ΔTMI = ΔRME ASA = ASA
MI = ME Corresponding parts of Congruent triangles are Congruent
answer: reasoning:
<E = <T given
M is the midpoint of TE given
TM = ME definition of a midpoint
<TMI = <RME property of Vertically Opposite Angles
ΔTMI = ΔRME ASA = ASA
MI = ME corresponding parts of congruent triangles are Congruent
hope this helps!
help me find the answer that bests best
represents this relationship
Answer:
c
Step-by-step explanation:
consider points (0,2) and (-4,0)
slope=(0-2)/(-4-0)=-2/-4=1/2
y-intercept=2
y=mx+c
y=1/2 x+2
Answer:
y=1/2x+2
Step-by-step explanation:
Write the following number in scientific notation. 788,000
Answer:
7.88 x 10^5 is 788,000 is scientific notation
A population grows according to an exponential growth model. The initial population is Po = 19 and the growth rate is r = 0.4.
Then find an explicit formula for Pn
Then use the formula to find P11
P11 equals 769.417 and general formula is 19*(1.4)^(n)
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself
The growth rate is .4 per time period.
the exponential growth model is f = p * (1 + .4) ^ n
f is the future value.
p is the present value.
r is the growth rate per time period.
n is the number of time periods.
in p0, n = 0
in p11, n = 11
you are given that p0 = 19
in the formula, that becomes f = 19 * (1 + .4) ^ 0 = 19 * (1.4) ^ 0 = 19.
the formula for p1 becomes f = 19 * (1 + .4) ^ 1 = 19 * (1.4) ^ 1 = 26.6
the formula for p11 becomes f = 19 * (1 + .4) ^ 11 = 19 * (1.4) ^ 11 = 769.417
the formula for pn becomes = 19*(1.4)^(n)
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Christie has $200 in her bank account. Every month, she deposits $20 into her account.
The equation of the line that models the amount of money, y, in her account x months from now is y = x .
Answer:
y = 20x + 200
Step-by-step explanation:
The 200 is the constant. It is only added once, but the monthly deposits are added at 20 every month.
After 1 month:
y = 20x + 200
y = 20(1) + 200
y = 20 + 200
y =220 money deposited.
After 2 months:
y = 20x + 200
y = 20(2) + 200
y = 40 + 200
y =240 money deposited.
After 3 months:
y = 20x + 200
y = 20(3) + 200
y = 60 + 200
y = 260 money deposited
And so on, and so on, and so on...
Lets find the digit in blank space of thr following numbers so hat the number formed is divisible by 11.
a.27.......3
What would the first step be in solving the equation 4/7x = 21
❄ Hi there,
the first step in solving this inequality is
multiplying (both sides) by 7[tex]\sf{\dfrac{4}{7}x\times7=21\times7}[/tex]. Look what happens on the left side!
[tex]\sf{4x=147}[/tex]
Multiplying both sides of an equation, or inequality, by the fraction's denominator, is a nice little trick when you need to get rid of fractions to solve in terms of a variable.
Finish solving for x by dividing both sides by 4 –
[tex]\sf{x=\dfrac{147}{4}}[/tex]
❄
The graph of the absolute value parent function
By the definition and properties of absolute value, there are two possible resulting functions: (i) g(x) = 5 · |x|, (ii) g(x) = |5 · x|. (Correct choices: B, D)
How to find a resulting function by applying rigid transformations
Herein we must modify a parent function to get a resulting function by the use of rigid transformations, defined as those transformations applied on geometric loci, including functions, such that Euclidean distance is conserved.
Based on the statement seen in the picture, the enlargement of the parent function can be done by a rigid transformation known as dilation, whose definition is shown below:
g(x) = k · f(x), where k is the stretch factor and is greater than 1. (1)
If we know that f(x) = |x| and k = 5, then the resulting function is:
g(x) = 5 · |x| (1)
This expression is also equivalent to the expression g(x) = |5 · x| by definition of absolute value.
By the definition and properties of absolute value, there are two possible resulting functions: (i) g(x) = 5 · |x|, (ii) g(x) = |5 · x|. (Correct choices: B, D)
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4. A store has 152 bottles of
water. This is 2 times the
number of sodas they
have. How many sodas
does the store have?
Answer:
76 sodas
Step-by-step explanation:
152 divided by 2
Answer: 76 sodas
Step-by-step explanation:
To find the sodas, use the data you see. Bottles of water are twice the sodas. So divided water by 2 to get the sodas.
152 ÷ 2 = 76 ( sodas ) . Hope it helps !
A spinner is labeled with the numbers 1,2,3,4,5,6,7,8, & 9.
Calculate the:
a. odds of spinning a 3
b. odds of not spinning a 9
c. odds of spinning an even number
d. odds of spinning a number less than 6
Answer:
Step-by-step explanation:
d
Find the future value in interest earned if $8704.56 is invested for eight years at 4% compounded semiannually
The future value interest earned semiannually at a compound rate of 4% is $7598.89.
To calculate the future value in interest earned, we use the of compound interest
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.
Formula:
I = [P(1+r/100)ⁿ-P]...................... Equation 1Where:
I = Future interestP = PrincipleR = Raten = Total timeFrom the question,
Given:
P = $8704.56r = 4%n = 2×8 = 16 semiannuallySubstitute the values above into equation 1
I = [8704.56(1+4/100)¹⁶-8704.56]I = 8704.56(1.04)¹⁶-8704.56I = 16303.48-8704.56I = $7598.89Hence, the future value interest earned is $7598.89.
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3. Working with Percent: Determine each amount. a) 1.6% of $150 b) 11.3% of $950 c) 0.29% of $2000 (3)
Answer:
a) (1,6 x 150)/100 = 2,4 dollars
b) (11,3 x 950)/100 = 107,35 dollars
c) (0,29 x 2000)/100 = 5,8 dollars
Researchers wanted to study if having a long beak is related to flight and birds they surveyed a total of 34 birds the data are shown in the contingency table below what is the relative risk of flying for those birds that have long beaks
The odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76.
What is an odds ratio?An odds ratio is a measure of the strength of an association with the exposure and outcome.
The odds ratio can be calculated by dividing the odds of the first group (exposure) by the odds of the second group (outcome).
Flies Does not fly Total
Long beak 11 7 19
Not a long beak 3 13 15
Total 14 20 34
Probability of long beaks flying = 0.79 (1/14)
Probability of not having long beaks flying = 0.21 (3/14)
Odds ratio = 3.76 (0.79/0.21)
Thus, the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76, showing greater odds of association.
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Complete question
Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 birds. The data are shown in the contingency table below. What is the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly? Round your answer to two decimal places.
Long beakNot a long beakTotalFlies11719Does not fly31315Total142034
When pricing out a menu, we know it is important to use the Edible a portion Price. What would the effect on your profit margin be, if we only used the as purchased price to determine our cost and selling price?
The effect of Edible a portion Price on your profit margin , if we only use the as purchased price to determine our cost and selling price is that it will maximize the profit because it will account for every part of the production.
What is edible portion cost?
The portion cost can be calculated by multiplying the cost of a usable kg with the portion size.
This can be represented as : portion cost = (portion size x cost of usable kg)
It should be noted that Edible portion (EP) serves as the portion of food which will be given top the customer after the preparation.
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Answer:
Step-by-step explanation:
Add (x^3 -2x^2+4) + (2x^3+x^2-2) express in standard form
Answer:
3x^3-x^2+0x+2Step-by-step explanation:
add both the equations then you will get
3x^3-x^2+2
but in the standard form there should be an x^1 term or x term since there is no term like that we write it as 0x
so the equation will be
3x^3-x^2+0x+2
The walls of a square room with side length s are being torn down and rebuilt. The area of the new room can be represented by 1.75s(2s + 3).
Which expression represents the area of the new room?
3.75s + 4.75
3.75s2 + 4.75s
3.5s2 + 5.25s
3.5s + 5.25
The expression that represents the area of the new room is (c) 3.5s^2 + 5.25s
How to determine the area of the new room?The given parameters are:
Wall =Square
Length = s
When the wall of the square room is torn down and rebuilt, the area of the new room is represented by 1.75s(2s + 3).
This means that
Area= 1.75s(2s + 3)
Expand the expression
Area= 1.75s * 2s + 1.75s * 3
Evaluate the products
Area= 3.5s^2 + 5.25s
This means that the expression that represents the area of the new room is (c) 3.5s^2 + 5.25s
Hence, the expression that represents the area of the new room is (c) 3.5s^2 + 5.25s
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5:
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The focal length of the given ellipse is given as (±6, 0)
Equation of an ellipseAn ellipse is defined as a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant or when a cone is cut by an oblique plane which does not intersect the base.
The standard equation of an ellipse is expressed as;
x^2/a^2 + y^2/b^2 = 1
The formula for calculating the focus of the ellipse is given as:
c^2 = b^2 - a^2
Given the equation of an ellipse
(x-7)^2/64 + (y-5)^2/100 = 1
This can also be expressed as:
(x-7)^2/8^2 + (y-5)^2/10^2 = 1
Comparing with the general equation
a = 8 and b = 10
Substitute
c^2 = 10^2 - 8^2
c^2 = 100 - 64
c^2 = 36
c = 6
Hence the focal length of the given ellipse is given as (±6, 0)
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Last month McKinneys Apothecary dispense the following liquid medication 1 gallon 3 quarts 7 pints and 3 dozens 6ounces of bottles in total how many millimeters what is dispensed
Answer: 10204 millimeters
Step-by-step explanation: A gallon = 3875 mm. A quart is 946. 946x 3 = 2838. A pint is around 473 mm which, when multiplied by 7, is 3311. Finally, there are 6 ounces which are approximately 30 mm. 6x30 = 180. We add all of this up : 3875 + 2838+ 3311 + 180 = 10204.
Write a linear function that passes through the points (3, -7) and (0, 15)
Answer:
The linear function for the given pts. will be
[tex]y = \frac{ - 22}{3}x + 15[/tex]
Step-by-step explanation:
Hello!
[tex]first \: find \: the \: slope \: for \: the \: two \: pts. \\ m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{(15 - ( - 7))}{(0 - 3)} where \: y2 = 15 \\ y1 = - 7 \\ x2 = 0 \\ x1 = 3 \\ m = \frac{ - 22}{3} \\ thus \: y = mx + b \: \: solve \: for \: b \: using \: one \: of \: the \: two \: points \\ lets \: take \: the \: second \: point \\ y = mx + b \\ 15 = \frac{ - 22}{3} (0) + b \\ b = 15 \\ therefore \: substitute \: this \: value \: to \: get \: the \: \\ y = \frac{ - 22}{3} x + 15[/tex]
What is the value of the last digit in 3,500.45
Answer:
five-hundredths
Step-by-step explanation:
In the similar quadrilaterals below, what angle corresponds to ∠C
HURRY PLEASE!!!
∠H
∠G
∠F
∠E
Answer:
angle G
Step-by-step explanation:
the quadrilateral did not change position or ration, it only shrank, so all the angles are in the same place and angle C = angle G
Answer:
2
Step-by-step explanation:
Use the ANOVA analysis tool Base on the given data uploaded, will you conclude that the number of bathroom of houses is a significant factor for house price? I your answer is affirmative, then explain how the house price is influenced by the number of bathroom?
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