Answer:
Step-by-step explanation:
If coins 110 plus 130 will give you 240 coins
If actual money 110 times 5 will give you 550 plus 130 will give you 680 or 6 dollars and 80 cents.
N times 5 plus p will be your equation
Let f: R - {2} => RX => f (x) = (3x + 4) / (x-2)Is F a bijection?
A function is called bijective if it is one-to-one and onto.
To check one to one, let x1 = x2 , where x1, x2 belongs to R.
so, we can say that:
[tex]3x_1+4=3x_2+4[/tex]and
[tex]x_1-2=x_2-2[/tex]Given the condition that x1 and x2 are not equal to 2. So, the above equation implies that
[tex]\frac{3x_1+4}{x_1-2}=\frac{3x_2+4}{x_2-2}\Rightarrow f(x_1)=f(x_2)[/tex]So, it is a one-to-one function.
For onto function, let y= (3x + 4) / (x-2). Now, interchange x and y, and solve the equation fo y:
[tex]\begin{gathered} x=\frac{3y+4}{y-2} \\ \Rightarrow xy-2x=3y+4 \\ \Rightarrow xy-3y=2x+4 \\ \Rightarrow y(x-3)=2x+4 \\ \Rightarrow y=\frac{2x+4}{x-3} \end{gathered}[/tex]Here, the domain of the inverse of the function is R - {3}. But the function is R - {2} => R. So, it is not onto.
thus, the given function is not a bijection.
In each of the following, describe the rate of change between the first pair and the second, assuming that the first coordinate is measured in minutes and the second coordinate is measured in feet. What are the units of your answer? (a) (2, 8) and (5, 17) (b) (3.4, 6.8) and (7.2, 8.7) (c) (3/2, - 3/4) and (1/4, 2)
The rate of change are:
a. 3 ft/min
b. 0.5 ft/min
c. -2.2 ft/min
How to Find the Rate of Change?The formula for finding the rate of change of a relationship is given as:
Rate of change = Change in y/change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
a. (2, 8) = [tex](x_1, y_1)[/tex]
(5, 17) = [tex](x_2, y_2)[/tex]
Rate of change = (17 - 8)/(5 - 2)
Rate of change = 9/3
Rate of change = 3 ft/min
b. (3.4, 6.8) = [tex](x_1, y_1)[/tex]
(7.2, 8.7) = [tex](x_2, y_2)[/tex]
Rate of change = (8.7 - 6.8)/(7.2 - 3.4)
Rate of change = 1.9/3.8
Rate of change = 0.5 ft/min
c. (3/2, - 3/4) = [tex](x_2, y_2)[/tex]
(1/4, 2) = [tex](x_2, y_2)[/tex]
Rate of change = (2 - (-3/4))/(1/4 - 3/2)
Rate of change = 11/4 / -5/4
Rate of change = 11/4 × -4/5
Rate of change = -11/5 = -2.2 ft/min
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a marksman has a probability of 0.268 for hitting a certain long-range target. what is the probability that it takes 5 shots for the marksman to hit the long-range target? (round your answer to three decimal places, if necessary.)
The probability of the marksman hitting the long-range target in 5 shots is 0.1429.
The geometric distribution is a Bernoulli experiment that predicts the likelihood of the first success after a certain number of failures. Negative-binomial and binomial distributions are two different forms of Bernoulli trials.
P = 0.268
x = 5
Use the geometric probability mass function below to calculate the probability:
P(X = x) = [tex](1 - P)^{(x-1)}[/tex]× P
P(X = x) = [tex](1 - 0.268)^{(3-1)}[/tex]× 0.268
P(X = x) = 0.1429
The probability that it takes 5 shots for the marksman to hit the long-range target is 0.1429.
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In the translation shown the image is
moved
A up 5
B down 5
C left 5
D right 5
the box contains 8 blue and 4 black pencils. 5 pencils are drawn at random from the box. find the probability that out of 5 pencils taken, 2 are blue and 3 are black.
The probability that out of 5 pencils taken, 2 are blue and 3 are black is 0.4381.
What is probability?Probability simply means the likelihood that something will occur or happen.
In this case, the the box contains 8 blue and 4 black pencils. The probability of drawing 2 blue balls will be:
= 8/12 × 7/11
= 0.4242
The probability of drawing 3 blacks will be:
= 4/12 × 3/12 × 2/12
= 1/3 × 1/4 × 1/6
= 0.0139
The probability will be the addition of the values. This will be:
= 0.4242 + 0.0139
= 0.4381
The probability is 0.4381.
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Complete the explanation of the error.
If x²=81, then x = 9.
The value of x could also be
The square root of a number can also be negative number so x could also be -9
Taking square root of a numberSquare root of a number is the number such that if it is multiplied by itself we get the square. The opposite of squaring an integer is finding its square root. As we know multiplication of two negative numbers produce a positive number. this is the reason why square of both positive and negative numbers are both positive. therefore, square root of a number can also be positive or neegative both. That is why we can't take square root of negative numbers.
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Find the distance between the points (-16, 20) and (-16, -14).2007(-16, 20)161284-20-16-12-8-4048121620-4-812(-16, -14)-16-20units
Point A
(-16, 20)
Point B
(-16, -14)
The Distance Formula itself is actually derived from the Pythagorean Theorem which is a
[tex]\begin{gathered} d=\sqrt[]{(y2-y1)^2+(x2-x1)^2} \\ d=\sqrt[]{(-14-20)^2+(-16-(-16}))^2 \\ d=\sqrt[]{(-34)^2} \\ d=34 \end{gathered}[/tex]The distance would be 34 units
Hello, I was wondering if the fraction 5/2 x and 5x/2 have the same value.
We have:
[tex]\frac{5}{2}x\text{ and }\frac{5x}{2}[/tex]These fractions are equal because the x is found by multiplying and it is as if we have this:
[tex]\frac{5}{2}\times\frac{x}{1}\text{ and }\frac{5\times x}{2}[/tex]And as we already know:
[tex]\frac{5}{2}\times\frac{x}{1}=\frac{5\times x}{2\times1}=\frac{5\times x}{2}=\frac{5x}{2}[/tex]Write the sum of 7√28x6 + 4√7x6 in simplest form, if x # 0
The sum equivalent to 7√28x⁶+4√7x⁶ is :
18√7x⁶ .
Solution:Remove parentheses and combine like terms to simplify each side of the equation.To isolate the variable term on one side of the equation, use addition or subtraction.To find the variable, use multiplication or division.Given ,7√28x⁶+4√7x⁶,
To find sum in simplest form ;
7√28x⁶+4√7x⁶
By splitting to factors,
= 7√(7*4)x⁶+4√7x⁶
= 7*2√7x⁶+4√7x⁶
= 14√7x⁶+4√7x⁶
By factoring out like terms,
= 2√7x⁶(7+2)
= 2√7x⁶(9)
= 18√7x⁶
Therefore sum is = 18√7x⁶.
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Given
\qquad \overline{BA}\perp\overline{BD}
BA
⊥
BD
start overline, B, A, end overline, \perp, start overline, B, D, end overline
\qquad m \angle CBD = 4x + 52^\circm∠CBD=4x+52
∘
m, angle, C, B, D, equals, 4, x, plus, 52, degrees
\qquad m \angle ABC = 8x - 10^\circm∠ABC=8x−10
∘
m, angle, A, B, C, equals, 8, x, minus, 10, degrees
Find m\angle CBDm∠CBDm, angle, C, B, D:
The value of ∠CBD is 68° and the value of ∠ABC is 22°
Given
Angle CBD = 4x + 52
Angle ABC = 8x − 10
If BA is perpendicular to BD, then ∠BAD = 90°
∠BAD = ∠CBD + ∠ABC
On substituting this values into the formula:
4x + 52 + 8x − 10 = 90
12x + 42 = 90
Add -42 to both sides
12x + 42 - 42 = 90 -42
12x = 48
x = 48/12
x = 4°
Here,
∠CBD = 4x + 52
∠CBD = 4 x 4 + 52 = 16 + 52 = 68°
Then,
∠ABC = 8x − 10
∠ABC = 8 x 4 − 10 = 32 - 10 = 22°
That is,
The value of ∠CBD is 68° and the value of ∠ABC is 22°
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Answer:
68 degrees
Step-by-step explanation:
got it right on khan academy
You want to go on a swamp tour. How long does it take a swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, from point Z to point S ?
If the swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, then the time taken to travel from point Z to point Y is 1.56 hours
The speed of the swamp vehicle = 3.2 miles per hour
From the figure we can see the two triangles ΔXVM and ΔXYZ
Here we have to use the ratio of the two similar triangles
The ratio will be
VW/WX = YZ/ZX
Substitute the values in the equations
10/6 = YZ/3
We have to find the distance from point Z to point Y
YZ = (10/6)×3
= 5 Miles
We know
Speed = Distance / Time
Time = Distance / speed
= 5/3.2
= 1.56 hours
Hence, if the swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, then the time taken to travel from point Z to point Y is 1.56 hours
The complete question is
You want to go on a swamp tour. How long does it take a swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, from point Z to point Y ?
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What is the equation of a line that passes though the Point (3, -7) and has a slope of -2?
Answer:
y = - 2x - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (3, - 7 ) into the partial equation
- 7 = - 6 + c ⇒ c = - 7 + 6 = - 1
y = - 2x - 1 ← equation of line
What is the length of the major axis of the conic section shown below? (x + 2)(y-1) 49 25 1
From the ellipse equation
[tex]\frac{(x+h)^2}{a^2}+\frac{(y+k)^2}{b^2}=1[/tex]the length of the major axis is equal to 2a. By comparing this equation with the given one, we can note that
[tex]\begin{gathered} a=7 \\ \text{because} \\ 7^2=49 \end{gathered}[/tex]Then, the length of the major axis is 2x7 = 14
Does anyone know the answers to this? I can’t figure it out
Answer:
[tex]y=57(0.88)^t[/tex][tex]\text{ \$}20.50[/tex]Explanation:
An exponential decay function is generally given in the below;
[tex]y=a\cdot(1-r)^t[/tex]where a = initial amount
r = percentage rate of decrease in decimal
t = number of years
Given the initial value of the book(a) as $57 and the percent decrease(r) as 12% which as a decimal is 0.12 (12/100), let's go ahead and substitute these values into the above formula and we'll have;
[tex]\begin{gathered} y=57(1-0.12)^t \\ y=57(0.88)^t \end{gathered}[/tex]When t = 8, let's go ahead and solve for y;
[tex]\begin{gathered} y=57(0.88)^8 \\ y=\text{ \$}20.50\text{ (to the nearest cent)} \end{gathered}[/tex]Don’t get how to do this
Answer:
1. 1.4, 1 5/8, 12/5, 8/8
2. 0.88
3. 1/4 and 8/8
4. 12/5 and 2/100
5. 1 5/8 and 1.625
6. 1 1/2
A bee flies at 9 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 18 minutes, and then flies directly back to the hive at 6 feet per second. It is away from the hive for a total of 22 minutes.
a. What equation can you use to find the distance of the flowerbed from the hive?
b. How far is the flowerbed from the hive?
Using the relation between velocity, distance and time, it is found that:
a. The equation used to find the distance of the flowerbed from the hive is: d = 540 feet per minute x 1.6 minutes.
b. The distance of the flower bed from the hive is: 864 feet.
Velocity, distance and timeVelocity is given by the distance divided by the time, as follows:
v = d/t
In the context of this problem, we have that:
The bee stays at the flowerbed for 18 minutes.The bee stays away from the hive for a total of 22 minutes.The times are as follows:
[tex]t_1[/tex]: hive -> flowerbed.[tex]t_2[/tex]: flowerbed -> hive.The sum of this times is of 22 - 18 = 4 minutes, hence:
[tex]t_1 + t_2 = 4[/tex]
During the first step, that is, from hive to flowerbed, the velocity is 1.5 times greater than during the second step, thus the second time is 1.5 times the first time, that is:
[tex]t_2 = 1.5t_1[/tex]
Then the first time is calculated as follows:
[tex]1.5t_1 + t_1 = 4[/tex]
[tex]2.5t_1 = 4[/tex]
[tex]t_1 = \frac{4}{2.5}[/tex]
[tex]t_1 = 1.6[/tex]
The velocity during this time was of 9 feet per second = 540 feet per minute, for 1.6 minutes, hence the equation is:
d = v x t
d = 540 feet per minute x 1.6 minutes.
d = 864 feet.
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question : below pictureis attached
Answer:
the value of 2/3 ^-2 is 18
15. Identify all of the acute angles shown.
A. ZXWZ, 2XYZ
B. There are no acute angles shown.
C. ZWZY, 2XWZ, ZWXY,
The identified acute angles in the diagram are: D. Angle WZY and angle WXY.
What are Acute Angles?An acute angle can be described as any angle that has a degree measure that is below 90 degrees, in order words, it is smaller than a right angle.
For example, an acute angle is attached below, which is 62°, and it is less than a right angle or 90 degrees. Angles 30°, 45°, 60°, 75°, etc are all regarded as acute angles because they are less than a right angle or 90 degrees.
In quadrilateral WXYZ, the acute angles that are less than a right angle, and are below 90 degrees are: D. Angle WZY and angle WXY.
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what is the probability that a card drawn randomly from a standard deck of 52 cards is a red three? express your answer as a fraction in lowest terms or a decimal number rounded to three decimal places, if necessary.
Answer:
1/26
Step-by-step explanation:
If the cards are all there, you can count there are 2 red threes. And there are 52 cards. The fraction is 2/52 or 1/26
4. multiple choice: as the sample size n increases, the distribution of sample means: a. becomes narrower b. remains constant c. becomes wider 5. multiple choice: according to the central limit theorem, the mean of the sample means is: a. less than the population mean b. the same as the population mean c. more than the population mean 6. multiple choice: according to the central limit theorem, the standard deviation of the sample means is: a. less than the population standard deviation b. the same as the population standard deviation c. more than the population standard deviation
The population mean, exists even comprehended as the average or mean of all values in a population, exist determined by summing all population values and dividing that total by the number of population values.
What is meant by the population mean?The population mean can be determined by dividing the total number of values in the given data/population by the sum of all values in the data/population. The whole sum of the numbers is referred to as summation. The sign μ stands for the population mean.
The population mean, also known as the average or mean of all values in a population, is determined by summing all population values (represented by the symbol X) and dividing that total by the number of population values (represented by the symbol N).
Therefore, the correct answer is option a. less than the population mean.
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Create an equivalent expression for 17^-7 • 17^5.
1/17²
1/17-²
17²
-17²
Please please pleaseee! I’m so dead if I don’t get this!
The equivalent expression for the indices is 17⁻⁷ × 17⁵ is 1/17²
How to create an equivalent expression for 17⁻⁷ × 17⁵?Index is the power or exponent which is raised to a number or a variable e.g in number 3⁵, 5 is the index of 3. The 3 is called the base. The plural form of index is indices.
We have different Laws of Indices, but the one applicable to this question is the product law and reciprocal law.
Product law: To multiply two variables or numbers with the same base, we need to add their powers and raise them to that base": 5² x 5³ = 5²⁺³ = 5 and P⁴ + P⁶ = P¹⁰
Reciprocal Law: If the index is a negative value, then it can be shown as the reciprocal of the positive index raised to the same variable:
8⁻² = 1/8² and b⁻⁶ = 1/b⁶
Let's use the two laws to create an equivalent expression for 17⁻⁷ × 17⁵:
17⁻⁷ × 17⁵ = 17⁻⁷ ⁺ ⁵ = 17⁻² = 1/17²
Therefore, the equivalent expression for 17⁻⁷ × 17⁵ is 1/17². The 1st option is the answer.
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12. Six hundred people will buy tickets at $4 each
for a district championship game. For each 20¢
decrease in price, 50 more people will buy
tickets. Find the best ticket price, the maximum
income, and the corresponding number of
tickets.
Using concept of Quadratic Equation we got that best ticket price is $16, maximum income is $19,200 and the corresponding number of tickets are 1200.
What is Quadratic Equation?A Quadratic Equation is one of the following: f(x) = ax2 + bx + c, where a, b, and c are positive integers and an is not equal to zero. A parabola is basically a curve that represents the graph of a quadratic equation. Parabolas can open up or down, and their "width" or "steepness" can vary, but they all have the same basic "U" shape.
We know that,
No. of people who will buy tickets at $4 = 600
For each 20¢ decrease, additional no. of people buying tickets = 50
Revenue = (No. of tickets sold)(Pricing)
Revenue = (600+50x)(4+x)
= 50[tex]x^{2}[/tex] + 800x + 2400
Solving the quadratic equation we got,
x = -4 or -12
Since we're dealing with real-life entities such as money, we'll take the value of x as positive.
Taking x as 12 (higher value),
No. of tickets sold = 600 + 50x = 1200
Pricing = 4 + x = 16
Revenue = 1200×16 = $19,200
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please dont use any big words & give an essay explanation
We want to create a real-life reasonable problem in which we can apply the laws of exponents.
Using a compound interest example;
Word Problem:
Calculate the final value of a $2,000 investment in an account with a 5% interest compounded Quarterly for 5 years.
Solving the word problem;
We have the following parameters;
[tex]\begin{gathered} \text{ Principal P = \$2,000} \\ \text{Rate r = 5\%} \\ \text{Time t = 5 years} \\ \text{ Number of times compounded n = 4} \end{gathered}[/tex]Recall that the formula for compound interest is;
[tex]F=P(1+\frac{r}{n})^{nt}[/tex]Substituting the given values;
[tex]\begin{gathered} F=2000(1+\frac{0.05}{4})^{4(5)} \\ F=2000(1+0.0125)^{20} \\ F=2000(1.0125)^{20} \\ F=2000\times(1.0125)^{20} \\ F=\text{ \$2,564.07} \end{gathered}[/tex]Therefore, the solution to the problem is;
The final
In the past, Quinn got paid $121,560 annually. Since switching to a new career, he has been making 55% less. How much does Quinn make now?
please help
Quinn got paid $121,560 in his first career and on switching, he made 55% less, i.e. he made 45% of his previous career.
This is because, if in a previous career he made 100%, then a 55% reduction in salary annually would mean, he is left with only 45%.
Let us suppose, previous salary as x
then, x= $121,560
so, 45% of x= 45% of $121,560
i.e. 45% of x= 45/100 x 121560
therefore, 45% of x= $54,702
Quinn makes $54,702 now.
Therefore, a reduction in 55% of earlier salary would mean that Quinn's salary reduced from $121,560 to $54,702
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cards are drawn from a deck (52 cards) until the first spades comes out. the eighth card drawn is the first spade. what is the probability the next card drawn is the ace of spades?
Probability that an ace is pulled from the deck = A/T=4/52=1/13
52 cards are there in all.
Four aces are found in all of the card A's.
Thirteen spades in all.
Probability that an ace is pulled from the deck = A/T=4/52=1/13
likelihood that a spade will be the next card drawn =S/T=13/52=1/4
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Yasmin is making some pancakes. Her recipe makes 6 pancakes.
Flour
Eggs
Milk
100g
2
250ml
Yasmin wants to make 15 pancakes.
Complete the table to show how much she will need of each ingredient.
a cup of all-purpose flour as an ingredient
White sugar, 2 tablespoons
Baking powder, two teaspoons
1 salt shaker, or as desired
a cup of milk
Vegetable oil, two tablespoons
1 beaten egg
How to make a pancakes?Directions
In a sizable basin, mix the flour, sugar, baking soda, and salt. Pour the milk, oil, and egg into the center well that has been created. Blend until uniform.
Over medium-high heat, preheat a griddle or frying pan with a little oil. For each pancake, pour or scoop about 1/4 cup of batter onto the griddle; cook for 1 to 2 minutes, or until bubbles form and the edges are dry. The opposite side should be browned after flipping. Use the leftover batter to repeat.
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a school nurse can give 25 eye tests in a two-hour period. how long will it take the nurse to give eye tests to all 600 stuents in her school.
can you take 73 devided by 17 and it be a whole number
an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 280280 engines and the mean pressure was 6.86.8 lbs/square inch. assume the standard deviation is known to be 0.90.9. if the valve was designed to produce a mean pressure of 6.76.7 lbs/square inch, is there sufficient evidence at the 0.050.05 level that the valve does not perform to the specifications? state the null and alternative hypotheses for the above scenario
We can infer that we have sufficient evidence to reject the null hypothesis and that the true mean is significantly lower than 6.7 at 10% of significance if we compare the p value and the significance level given =0.05 and observe that p'.
What is the meant by hypothesis test?Hypothesis test: A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters thanks to hypothesis testing.
Data are provided and noted.
X=6.8 display the sample mean
σ= 0.9 show the population's standard deviation.
n= 280 samples taken
μο=6.7 the value that we wish to test should be represented
α=0.1 signify the hypothesis test's level of significance.
The stat would be represented as z. (variable of interest)
p' indicate the test's p value (variable of interest)
Name the prevailing and competing hypothesis
The system of hypothesis must be tested to see if the true mean is below the criteria.
Null hypothesis: μ ≥ 6.7
Alternative hypothesis: μ < 6.7
Applying a z test to compare the actual mean to the reference value is preferable if the sample size is greater than 30 and we are aware of the population variation. The statistic is given by:
z=(X-μο)/σ[tex]\sqrt{n}[/tex] ......(1)
z-test: "enables the comparison of group means. One of the most widely used tests, it is used to determine whether the mean is (higher, lower, or not equal) to a given value ".
Calculate the statistic
We can replace in formula (1) the info given like this:
z=(6.8-6.7)/0.9[tex]\sqrt{280}[/tex]
P-value
Since is a one sided test the p value would be:
p'=p(z<0.0066)
We can infer that we have sufficient evidence to reject the null hypothesis and that the true mean is considerably lower than 6.7 at 10% of significance if we compare the p value and the significance level given =0.1 and observe that p'.
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Which statement best describes how to slice a cone so that the resulting cross section is an ellipse
Cutting at less than a right angle to the axis but more than the angle made by the side of the cone produces an ellipse.
Therefore, with this above statement, the statement which best describes how to slice a cone so that the resulting cross-section is an ellipse is
A plane slicing the cone diagonally without intersecting the base
The correct option, therefore, is OPTION B
