Given:
A lab assistant needs to create a 1000 ML mixture that is 5% hydroelectric acid.
The assistant has solutions of 3.5% and 6% in supply at the lab.
let the number of milliliters from the solution of 3.5% = x
And the number of milliliters from the solution of 6% = y
so, we can write the following equations:
The first equation, the sum of the two solutions = 1000 ml
So, x + y = 1000
The second equation, the mixture has a concentration of 5%
so, 3.5x + 6y = 5 * 1000
So, the system of equations will be as follows:
[tex]\begin{gathered} x+y=1000\rightarrow(1) \\ 3.5x+6y=5000\rightarrow(2) \end{gathered}[/tex]Now, we will find the solution to the system using the substitution method:
From equation (1)
[tex]x=1000-y\rightarrow(3)[/tex]substitute with (x) from equation (3) into equation (2):
[tex]3.5\cdot(1000-y)+6y=5000[/tex]Solve the equation to find (y):
[tex]\begin{gathered} 3500-3.5y+6y=5000 \\ -3.5y+6y=5000-3500 \\ 2.5y=1500 \\ y=\frac{1500}{2.5}=600 \end{gathered}[/tex]substitute with (y) into equation (3) to find x:
[tex]x=1000-600=400[/tex]So, the answer will be:
Enter the equations below separated by a comma
[tex]x+y=1000,3.5x+6y=5000[/tex]How many milliliters of the 3.5% solution should be used?
400 milliliters
How many milliliters of 6% solution should be used?
600 milliliters
NO LINKS!! Please help me with this probability question 2a
====================================================
Work Shown:
A = he eats pizza
B = he drinks cola
P(A) = 0.40
P(B) = 0.60
P(A and B) = 0.30
Then apply the conditional probability formula.
P(A given B) = P(A and B)/P(B)
P(A given B) = 0.30/0.60
P(A given B) = 0.5 exactly
P(A given B) = 50%
If we know for certain he drinks cola, then there's a 50% chance of him eating pizza.
n a recent poll, a random sample of adults in some country (18 years and older) was asked, "When you see an ad emphasizing that a product is "Made in our country," are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?" The results of the survey, by age group, are presented in the following contingency table. Complete parts (a) through (c).
Purchase likelihood
Total
Total
Question content area bottom
Part 1
(a) What is the probability that a randomly selected individual is years of age, given the individual is to buy a product emphasized as "Made in our country"?
The probability is approximately
0.134.
(Round to three decimal places as needed.)
Part 2
(b) What is the probability that a randomly selected individual is to buy a product emphasized as "Made in our country," given the individual is years of age?
The probability is approximately
a) The probability that a randomly selected individual is 45-54 years of age, given the individual is neither more nor less likely to buy is 0.206
b) The probability that a randomly selected individual is neither more nor less likely to buy, given the individual is 45-54 years of age is 0.309
c) 18-34 year olds are less likely to buy a product emphasized as "Made in our country" than individuals in general.
Hence, the answer is no.
A random sample is one that is drawn at random from the population, meaning that every member of the population has an equal chance of being picked for the sample. The probability sampling approach is the practice of choosing people at random.
a. Total number of individuals that are neither more nor less likely to purchase = 786
Total number of individuals aged 45-54 that are neither more nor less likely to purchase = 162
The probability that a randomly selected individual is 45-54 years of age, given the individual is neither more nor less likely to buy =
= Total number of individuals aged 45-54 neither more or less likely to purchase./ Total number of individuals more or less likely to purchase.
= 162/786
= 0.206
b. Total number of individuals 45-54 years of age = 524
Total number of individuals aged 45-54 that are neither more nor less likely to purchase = 162
The probability that a randomly selected individual is neither more nor less likely to buy, given the individual is 45-54 years of age
= Total number of individuals aged 45-54 neither more or less likely to purchase./ Total number of individuals 45-54 years of age.
= 162/524
= 0.309
c. The number of 18-34 year old individuals more likely to buy = 204
The total number of 18-34 year old individuals = 523
The proportion of 18-34 year old individuals more likely to buy = 204/523
= 0.390
= 39%
The total number of individuals more likely to buy = 1266
The total number of all individuals in the survey = 2123
The proportion of individuals, in general, more likely to buy = 1266/2123
= 0.596
= 59.6%
Therefore, 18-34 year olds are less likely to buy a product emphasized as "Made in our country" than individuals in general.
Hence, the answer is no.
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Your question is incomplete. Please find the missing content below.
In a recent poll, a random sample of adults in some country (18 years and older) was asked, "When you see an ad emphasizing that a product is "Made in our country," are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?" The results of the survey, by age group, are presented in the following contingency table. Complete parts (a) through (c).
Purchase likelihood 18-34 35-44 45-54 55 and over Total
More likely 204 318 334 410 1266
Less likely 27 5 28 11 71
Neither more nor less 292 210 162 122 786
Total 523 533 524 543 2123
a) What is the probability that a randomly selected individual is 45-54 years of age, given the individual is neither more nor less likely to buy a product emphasized as "Made in our country"? The probability is approximately _____. (round to three decimal places)
b) What is the probability that a randomly selected individual is neither more nor less likely to buy a product emphasized as "Made in our country", given the individual is 45-54 years of age? The probability is approximately _____. (round to three decimal places)
c) Are 18-34-year-olds more likely to buy a product emphasized as "Made in our country" than individuals in general? Yes or no
The cost C (in dollars) of producing x units of a product is given by the following. C= 2.6. Square root of x + 600
The marginal cost in dollars of producing x units is given by the next equation:
[tex]C=2.6\sqrt[]{x}+600[/tex]a)
To find the marginal cost (in dollars per unit) when x= 9.
Then, we need to replace x=9 on the derivation of the cost equation:
So:
[tex]\frac{d}{dx}C=\frac{1.3}{\sqrt[]{x}}[/tex]Where:
[tex]\frac{d}{dx}2.6\sqrt[]{x}=2.6\frac{d}{dx}\sqrt[]{x}=2.6\frac{d}{dx}^{}x^{\frac{1}{2}}=2.6\cdot\frac{1}{2}x^{\frac{1}{2}-1}=1.3\cdot x^{-\frac{1}{2}}=\frac{1.3}{\sqrt[]{3}}[/tex]and, the derivate of a constant is equal to zero.
[tex]\frac{d}{dx}600=0[/tex]Replacing x= 9
[tex]\frac{d}{dx}C=\frac{1.3}{\sqrt[]{9}}[/tex]Hence, the marginal cost is equal to:
[tex]\frac{d}{dx}C=0.43[/tex]b) Now, when the production increases 9 to 10. It's the same as the cost of producing one more machine beyond 9.
Then, it would be x=10 on the cost equation:
[tex]C=2.6\sqrt[]{x}+600[/tex][tex]C=2.6\sqrt[]{10}+600[/tex][tex]C=608.22[/tex]and x= 9
[tex]C=2.6\sqrt[]{9}+600[/tex][tex]C=2.6(3)+600[/tex][tex]C=607.8[/tex]Then, we calculate C(10) - C(9) =
[tex]608.22-607.8[/tex][tex]=0.43[/tex]C)
Both results are equal.
Hence, the marginal cost when x=9 is equal to the additional cost when the production increases from 9 to 10.
An emperor penguin has
76,634 feathers. The penguin has about 27 times as many feathers as a blue jay.
About how many feathers does the blue jay have?
Answer:
2,842 feathers
Step-by-step explanation:
An emperor penguin has 76,634 feathers. The penguin has about 27 times as many feathers as a blue jay. About how many feathers does the blue jay have?
76,634/27 = 2,842 feathers
I need help me answering #10 I'm really bad with ratios. (also sorry for the bad lighting in the picture)
The ratio of Perch to total fish is:
3 ( Number of perch that he caught)
------------------------------------------------------
9 ( The result of the addition of all values)
Simplifying, we have:
1
---
3
So, the answer would be 1 : 3
look at the screenshots
Answer:
c for the first one and a for the second
Write the equation of a quadratic in general form, given its solutions.x=4 ; x=-1
The given solutions of the quadratic equation:
x = 4 and x = -1
First we make them factors of the equation:
x= 4 becomes:
[tex]x-4\text{ = 0}[/tex]and x = -1 becomes:
[tex]x\text{ + 1 = 0}[/tex]So (x-4) and (x+1) are the factors.
To get the general quadratic equation, we would expand the factors
[tex]\begin{gathered} (x-4)(x+1)\text{ = 0 } \\ x(x+1)\text{ -4(x+1) = 0} \\ x^2+x\text{ -4x-4 = 0} \end{gathered}[/tex][tex]\begin{gathered} Adding\text{ like terms} \\ x^2-3x-4\text{ = 0} \end{gathered}[/tex]The general quadratic equation:
[tex]x^2\text{ - 3x - 4 = 0}[/tex]Tristan tried his luck with the lottery. He can win $85 if he can correctly choose the 3 numbers drawn. If order matters and there are 13 numbers in the drawing, how many different ways could the winning numbers be drawn?
The ways to select the winning numbers is 286
How to determine the ways the winning numbers could be drawn?From the question, we have
Total numbers, n = 13Numbers to select, r = 3The winning numbers could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 13 and r = 3
Substitute the known values in the above equation
Total = ¹³C₃
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 13!/10!3!
Evaluate
Total = 286
Hence, the number of ways is 286
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Khalid is investigating two linear functions. The first linear function is defined by the equation 2x + 3y = 12. The second linear functionpasses through the points (3,-2) and (-2, k).For the case where the two linear functions have the same y-intercept, what must be the value of k?k=
According to the given data we have the following:
first linear function is defined by the equation 2x + 3y = 12
second linear function passes through the points (3,-2) and (-2, k)
the two linear functions have the same y-intercept
k?
To calculate k first we have to do the following:
we would have to use the formula y=mx +b
the two linear functions have the same y-intercept, therefore, b=12.
So, y=mx +12
As second linear function passes through the points (3,-2) we are going to substitue the x and y with 3 and -2.
So, -2=m*3+12
-2-12=m*3
-14=m*3
m=-14/3
m=-4
Finally we would calculate k by writiing the equation of the line that passes through each pair of points as follows:
y2-y1/x2-x1=m
So
[tex]\frac{k\text{ -(-2)}}{\text{-2 - 3}}\text{ }=\text{ -4}[/tex]So, k +2/-5=-4
k+2=20
k=20-2
k=18
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided
From the given picture we can see
ACB is a right triangle at C
AC = b
CB = a
AB = c
Since mSince a = 5 ft
Then to find b and c we will use the trigonometry ratios
[tex]\begin{gathered} \sin A=\frac{a}{c} \\ \sin 60=\frac{5}{c} \end{gathered}[/tex]Substitute the value of sin 60
[tex]\begin{gathered} \sin 60=\frac{\sqrt[]{3}}{2} \\ \frac{\sqrt[]{3}}{2}=\frac{5}{c} \end{gathered}[/tex]By using the cross multiplication
[tex]\begin{gathered} \sqrt[]{3}\times c=2\times5 \\ \sqrt[]{3}c=10 \end{gathered}[/tex]Divide both sides by root 3
[tex]\begin{gathered} \frac{\sqrt[]{3}c}{\sqrt[]{3}}=\frac{10}{\sqrt[]{3}} \\ c=\frac{10}{\sqrt[]{3}} \end{gathered}[/tex]To find b we will use the tan ratio
[tex]\begin{gathered} \tan 60=\frac{a}{b} \\ \tan 60=\frac{5}{b} \end{gathered}[/tex]Substitute the value of tan 60
[tex]\begin{gathered} \tan 60=\sqrt[]{3} \\ \sqrt[]{3}=\frac{5}{b} \end{gathered}[/tex]Switch b and root 3
[tex]b=\frac{5}{\sqrt[]{3}}[/tex]The exact values of b and c are
[tex]\begin{gathered} b=\frac{5}{\sqrt[]{3}} \\ c=\frac{10}{\sqrt[]{3}} \end{gathered}[/tex]Find the equation of the line passing through the points (-11,-18) and (-22,-16). Write your answer in the
form y = mx + b.
Answer: y =
Write your answers as integers or as reduced fractions in the form A/B.
Answer:
y=−2/11x−20
Step-by-step explanation:
A bourse named northern dancer won the Kentucky derby by running 1 1/4 miles in exactly 2 minutes. At this constant rate, how long does it take northern dancer to run the 1 1/2 mile Belmont stakes? Use unit rate
It is given that there are
[tex]1\frac{1}{4}=\frac{5}{4}\text{miles}[/tex]run in 2 minutes.
So, we have to determine time required to run
[tex]1\frac{1}{2}=\frac{3}{2}\text{miles}[/tex]Apply the unitary method,
For 5/4 miles required 2 minutes.
So , for 1 miles, time required
[tex]\frac{2}{\frac{5}{4}}=\frac{2\times4}{5}=\frac{8}{5}\min [/tex]Therefore,for 3/2 miles , time required is
[tex]\frac{3}{2}\times\frac{8}{5}=\frac{12}{5}\text{min}=2.4\min [/tex]Hence the time required is 2.4 minutes.
The perimeter of a living room is 68 feet.if the length of the living room is 18 feet what is the width of the living room
the perimeter of a cuadrilateral is 2L+2W=68 where L is the length of the room
since L= 18 feet
we will have that
2(18)+2W=68
then
W=(68-36)/2= 32/2=16
Therefore, the width of the living room is 16 feet.Higher Order ThinkingIn 448,244, how is the relationship between the first pair of 4s the same as the relationship between the second pair of 4s?4 grade studentLesson place value relationship
In the number 44,244, we can see two pairs of 4's.
The first pair (to the left) has a higher value than the second pair to the right, but the 4's have something in common: The leftmost 4 is ten times as high as the rightmost 4.
For this reason, we start the number as forty-four thousand and end up with forty-four.
There are 6 dogs and 2 mice. Write a ratio for the number of ears to th number of paws. * 6:2 3 people are in a room. Write a ratio to represent the number of finger
each dog has 4 paws, then 6 dogs have 6*4 = 24 paws
each mouse has 4 paws, then 2 mice have 2*4 = 8 paws
Total number of paws: 24 + 8 = 32 paws
each dog has 2 ears, then 6 dogs have 6*2 = 12 ears
each mouse has 2 ears, then 2 mice have 2*2 = 4 ears
total number of ears: 12 + 4 = 16 ears
The ratio for the number of ears to the number of paws: 16/32 = 1/2 or 1:2
The length of the diagonal of a Rectangle is 14cm,and it forms a 30 degree angle in one corner of the rectangle.What is the area of the rectangle.(A=LxW)
We can find W and L using the sine and the cosine functions:
[tex]\begin{gathered} \sin (30)=\frac{W}{14} \\ so\colon \\ W=14\cdot\sin (30) \\ --------- \\ \cos (30)=\frac{L}{14} \\ so\colon \\ L=14\cdot\cos (30) \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} A=L\cdot W \\ A=14\cdot\cos (30)\cdot14\cdot\sin (30) \\ A=49\sqrt[]{3} \\ A\approx84.87cm^2 \end{gathered}[/tex]Answer:
84.87 cm²
algebra 2 question..
We are supposed to solve the equation
[tex]6(2x-1)-12=3(7x+4)[/tex]Here, we need to apply the distributive laws on both sides.
Comment: The distributive laws say that
[tex]a(b+c)=ab+ac\text{ and }(b+c)a=ba+ca[/tex]Using this comment we get
[tex]6(2x-1)=6(2x)+6(-1)=12x-6[/tex][tex]3(7x+4)=3(7x)+3(4)=21x+12[/tex]Then, our equation becomes
[tex](12x-6)-12=21x+12[/tex][tex]12x-18=21x+12[/tex]Now, let's apply the rule: terms with x on the right-hand side, and the rest on the left-hand side, to obtain
[tex]-18-12=21x-12x[/tex][tex]-30=9x[/tex][tex]x=\frac{-30}{9}=-\frac{10}{3}[/tex]Drag each tile to the correct box.The figures in the graph below can be shown to be similar by a sequence of transformations.Choose the correct sequence of transformations that take figure A to figure B.
Answer
Rotate 270 degrees clockwise about the origin → Translate 3 units right and 3 units up → Dilate by a scale factor of 3
Step-by-step explanation
Rotation 270 degrees clockwise about the origin transforms the point (x, y) into (-y, x). Applying this rule to the vertices of figure A, we get:
(-5, 5) → (-5, -5)
(-4, 4) → (-4, -4)
(-5, 1) → (-1, -5)
(-4, 1) → (-1, -4)
Translation 3 units right and 3 units up transform the point (x, y) into (x+3, y+3). Applying this rule to the previous points, we get:
(-5, -5) → (-5+3, -5+3) → (-2, -2)
(-4, -4) → (-4+3, -4+3) → (-1, -1)
(-1, -5) → (-1+3, -5+3) → (2, -2)
(-1, -4) → (-1+3, -4+3) → (2, -1)
Dilation by a factor of 3 transforms the point (x, y) into (3x, 3y). Applying this rule to the previous points, we get:
(-2, -2) → (3x-2, 3x-2) → (-6, -6)
(-1, -1) → (3x-1, 3x-1) → (-3, -3)
(2, -2) → (3x2, 3x-2) → (6, -6)
(2, -1) → (3x2, 3x-1) → (6, -3)
These vertices coincide with the vertices in figure B
Use the remainder theorem to find P (1) for P(x) = 2x - 3x' + 3x -3.Specifically, give the quotient and the remainder for the associated division and the value of P (1).미미2Quotient = 0Х$2Remainder =0P(1) =
Using the remainder theorem, we must find P(1) for:
[tex]P(x)=2x^4-3x^3+3x-3[/tex]1) Because we want to evaluate P(x) for x = 1, we must compute
[tex]\frac{2x^4-3x^3+3x-3}{x-1}[/tex]2) Now we make the synthetic division by putting a 1 in the division box:
The remainder from the division is:
[tex]R=-1[/tex]The quotient of the division is:
[tex]2x^3-x^2+2x+2[/tex]3) From the synthetic division we get a remainder R = -1, applying the Remainder Theorem we get that:
[tex]P(1)=R=-1[/tex]Summary
The answers are:
1)
[tex]Quotient=2x^3-x^2+2x+2[/tex]2)
[tex]Remainder=-1[/tex]3)
[tex]P(1)=-1[/tex]Shawna is making smoothies. The recipe calls for 2 parts yogurt to 3 parts
blueberries. Shawna wants to make 10 cups of smoothie mix. How many cups of
yogurt and blueberries does Shawna need?
Answer: 4 part yogurt 6 part blueberries
Step-by-step explanation: 2+3=5 5x2=10 3x2=6 2x2=4 6+4=10
A commercial citrus farm has decided to mechanise the planting operation. A tractor was
purchased that can plant and water seedlings automatically with pneumatic tubes. In order to
ensure the saplings receive the correct amount of water, a maximum variance of 55mm2
is
tolerated when watering. A sample of 31 planting lines were measured and the variance was
found to be 68mm2
. Test at 1% level of significance if the tractor is not operating correctly.
From the checks and calculation the tractor is not operating correctly.
What is standard deviation?Standard deviation refers to by how how much the data varies from the mean
How to determine if the tractor is not operating correctlyGiven data form the question
1% level of significance
variance was found to be 68mm2
A sample of 31 planting lines
a maximum variance of 55mm2
Definition of variables
1% level of significance is equivalent to 99% confidence interval
mean sample, μ = ?
standard deviation, SD = √variance = √68 = 8.246
Z score, Z = 2.576
from z table z score of 99%confidence interval = 2.576sample size, n = 31
maximum variance, X = 55mm2
The formula in term s of Z is
Z = ( X - μ ) / SD
2.576 = (55 - μ) / 8.246
(55 - μ) = 2.576 * 8.246
55 - μ = 21.242
μ = 55 - 21.242
μ = 33.758 mm²
For the tractor to be working correctly the difference between the mean and 2 * SD should not be more than the maximum variance which is 55mm²
55mm² ≥ mean ± 2 * SD
55mm² ≥ 33.758 mm² ± 2 * 8.246
55mm² ≥ 50.25
Since 50.25 is less than the maximum variance the tractor is operating correctly
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55mL of hardener to each container of resin. How much hardener should be added to 14 containers of resin?Write your answer in liters.
The amount of hardener added to 1 container of resin = 55mL.
The amount of hardener added to 14 containers is calculated as,
[tex]\begin{gathered} \text{Amount of hardener = 55 }\times\text{ 14 } \\ \text{Amount of hardener = 770 mL} \\ \text{Amount of hardener = 0.770 L} \end{gathered}[/tex]Thus 0.770 litres of hardener must be added to 14 containers of resin.
what is 5/6 converted to decimal form
5/6 in decimal form is
[tex]\frac{5}{6}=0.8\bar{3}[/tex]the sales tax is 47 on the purchase of a dining room set for 940. find the sales tax rate.
The sales tax formula is used to determine how much businesses need to charge customers based on taxes in their area. State and local governments across the United States use a sales tax to pay for things like roads, healthcare and other government services. Sales tax applies to most consumer product purchases and exists in most states.
The sales tax formula is simply the sales tax percentage multiplied by the price of the item. It's important for businesses to know how to use the sales tax formula so that they can charge their customers the proper amount to cover the tax. For consumers, it's good to know how the sales tax formula works so that you can properly budget for your purchases
The sales tax formula is as shown below:
[tex]\text{sales tax=sales tax percentage }\times Price\text{ of the items}[/tex]Given that
Sales tax = 47
price of the dining room = 940
Sales tax rate= unknown
To find the sales tax rate, we would substitute into the formula above
[tex]\begin{gathered} 47=\text{sales tax rate }\times940 \\ \text{sales tax rate = }\frac{47}{940}\times100\text{ \%} \\ \text{sales tax rate = }\frac{1}{20}\times100=0.05\times100\text{ \%} \\ \text{sales tax rate= 5 \%} \end{gathered}[/tex]Hence, the sales tax rate is 5%
What is the product of 11/12 and its reciprocal?
Answer:
The product of 11/12 is 0.916.This as as a fraction would be 0.916/1.00. This means it's reciprocal is 1.
Step-by-step explanation:
The reciprocal is basically the bottom part, denominator, of the fraction, being siwtched to on top of the fraction (numerator, and vice versa. The fraction would be 0.916/ 1.00 because the closest whole number to 0.916 is 1, meaning the fraction would be 0.916 out of 1. DO NOT MISTAKE THIS FOR 100. When you do the final step, finding the recirprocal of 0.916/1.00, we siwtch the numerator and denominators position, making out answer:
The product of 11/12 is 0.916 which is 0.916/1.00 in fraction form. The reciprocal of this is 1.00/0.916. Hope this helped!
Determine whether the following relation is a function. Then state the domain and range of the relation or function.{(7,6), (4,-6), (0,-1), (3,3), (1,1)}Is this relation a function? Choose the correct answer below.A.Yes, because each first component corresponds to exactly one second component.B.No, because each first component corresponds to more than one second component.C.Yes, because each first component corresponds to more than one second component.D.No, because each first component corresponds to exactly one second component.
A function is a relation in which each possible input value leads to exactly one output value. We say “the output is a function of the input.”
The input values make up the domain, and the output values make up the range.
The relation is given to be:
[tex]\mleft\lbrace(7,6\mright),(4,-6),(0,-1),(3,3),(1,1)\}[/tex]To classify a function, get the input and output values. If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.
The input values are: {7, 4, 0, 3, 1}
The output values are: {6, -6, -1, 3, 1}
Therefore, the relation is a function.
The correct option is OPTION A: Yes, because each first component corresponds to exactly one second component.
The domain is:
[tex]\mleft\{7,4,0,3,1\mright\}[/tex]The range is:
[tex]\mleft\{6,-6,-1,3,1\mright\}[/tex]The pro shop at the Hidden Oaks Country Club ordered two brands of golf balls. Swinger balls cost$2.10 each and the Supra balls cost $1.00 each. The total cost of Swinger balls exceeded the total costof the Supra balls by $330.00. If an equal number of each brand was ordered, how many dozens ofeach brand were ordered?AnswerHow to enter your answer (opens in new window)KeypadKeyboard Shortcutdozen
The Solution:
Given that equal number of each brand of golf ball was ordered.
Let the number of each brand ordered be represented with n
Each swinger ball cost $2.10
So, the total cost of the swinger ball ordered is:
[tex]2.10n[/tex]Each Supra ball cost $1.00
So, the total cost of the supra ball ordered is:
[tex]\begin{gathered} 1.00\times n \\ \text{which becomes}\colon \\ n \end{gathered}[/tex]Given that the total cost of the Swinger balls exceeded the total cost of the Supra balls by $330.00. We have the linear equation below:
[tex]2.1n=n+330[/tex]We are required to find the number of dozens of each brand of golf balls that were ordered.
So, we shall solve for n and then divide the value by 12.
[tex]\begin{gathered} 2.1n=n+330 \\ \text{collecting the like terms, we get} \\ 2.1n-n=330 \\ 1.1n=330 \end{gathered}[/tex]Dividing both sides by 1.1, we get
[tex]\begin{gathered} \frac{1.1n}{1.1}=\frac{330}{1.1} \\ \\ n=300\text{ balls} \end{gathered}[/tex]Dividing 300 by 12 (since 1 dozen = 12 balls), we get
[tex]\frac{300}{12}=25\text{ dozens of each brand of golf balls were ordered.}[/tex]Therefore, the correct answer is 25 dozens.
is this right triangle shown a right triangle? 50 cm2 40mc2 20cm2 Explain your reasoning.
Solution:
Note that :
[tex]2500=50^2\ne\text{ }40^2+20^2=2000[/tex]and If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. In this case, this statement is not true. We can conclude that it is not a right triangle.
Solve each system of equations please show your work! 3x+y-2z=22 x+5y+z=4 x=-3z
The solution of the system of equations are x = - 6 , y = 44 and z = 2
Given,
The system of equations;
3x + y - 2z = 22
x + 5y + z = 4
x = -3z
We have to solve the given equations;
Substitute x = -3z in both equations;
3x + y - 2z = 22
⇒ 3 × -3z + y - 2z = 22
⇒ - 9z + y - 2z = 22
⇒ - 11z + y = 22
And,
x + 5y + z = 4
⇒ - 3z + 5y + z = 4
⇒ 5y - 2z = 4
Solve the equations - 11z + y = 22 and 5y - 2z = 4
We get,
⇒ y = 44 and z = 2
So, x = - 3z
⇒ x = - 3 × 2
⇒ x = - 6
Thus, The solution of the system of equations are;
⇒ x = - 6 , y = 44 and z = 2
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A Geiger counter counts the number of alpha particles from radioactive material. Over a
long period of time, an average of 16 particles per minute occurs. Assume the arrival of
particles at the counter follows a Poisson distribution. Round your answers to four decimals.
a) Find the probability of exactly 21 particles arrive in a particular one minute period.
0.0426053 O
b) Find the probability of exactly one particle arrives in a particular one second period.
0.20424755689724
a) The probability of exactly 21 particles arrive in a particular one minute period is 0.0426
b) The probability of exactly one particle arrives in a particular one second period is 0.2042
What is probability?Probability is the ratio of the total number of conceivable outcomes to the number of outcomes in an exhaustive set of equally likely alternatives that result in a particular occurrence.
The probability is given by:
P(X=x) = (e⁻ⁿ nˣ)/x!
a) The probability of exactly 21 particles arrive in a particular one minute period is given by :
P(X=21) = (e⁻16 × 16²¹)/21!
P(X=21) = (2.176746853×10¹⁸)/51090942171709440000
P(X=21) = 0.0426
b) The probability of exactly one particle arrives in a particular one second period is :
1 min = 16 particles
1 sec = 16/60 particles
1 sec = 0.2667 particles
P(X=1) = (e⁻⁽¹⁶/⁶⁰⁾ × (16/60)¹)/1!
P(X=1) = 0.2042
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