Answer:
4/13
Step-by-step explanation:
There are 4 jacks in the deck and 13 spades. However 1 jack is a spade so we have a total of 16 cards which are either a jack or a spade. Therefore there are (13 + 4 - 1)/52 cards which are not a jack or a spade. Divided 16/52, thus the probability is 4/13.
The probability of drawing a spade or a jack from a standard deck of 52 cards is;
P(drawing either a spade or jack) = 4/13
We are told that the standard deck of cards has 52 cards.
Thus;
N = 52
Now,in a pack of cards there are usually 4 Jacks and 13 spades.
However, among the 4 Jacks, 1 of them is a spade. This means that 1 card will be both a spade and a jack. Thus,
Possible number of Jack's and spades = 13 + 4 - 1 = 16
Thus;
P(drawing either a spade or jack) = 16/52 = 4/13
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Kingston obtained a loan for $1,000 to be paid back in 30 days. The lender quoted Kingston a $200 fee. Which of the following statements is correct regarding this loan?
Answer:
A The APR is over 240%.
Step-by-step explanation:
Given:
Loan amount = $1000Time = 30 daysRate = $200 per 30 daysNow options:
A The APR is over 240%.
Correct since $200 per 30 days ⇒ 20% per 30 days ⇒ 240$ per 360 days ⇒ more than $240 for yearB The fee will be paid only if Kingston makes a late payment.
Incorrect. This is the sum to be paid at the end of 30 daysC The $1,000 plus finance charges will be paid at the end of one year.
Incorrect. All charges including the loan due paid at the end of 30 daysD Kingston will receive $1,200 from the loan.
Incorrect. Loan amount is $1000`.Answer:
A The APR is over 240%.
Step-by-step explanation: Hope this helps ya'll
5. 2x + 5 - 7x = 15
6.
X=
Help me
Answer:
-2
Step-by-step explanation:
2x+5-7x=15
Combine like terms
-5x+5=15
Subtract 5 from both sides
-5x=10
Divide -5 from both sides
x=-2
Answer:
2x+5-7x=15
-5x+5=15
5-15 =5x
-10 =5x
10/5=x
x= -2
Name the intersection of plane ABC and plane LOD
Answer:
segment AD
Step-by-step explanation:
LOD is the far side of the cube.
ABC is the left side.
So the intersection is the vertical EDGE AD, on the far-left.
The two planes ABC and LOD intersect each other at the segment AD.
What is the coordinate plane?A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.
Given that there is a cube made of six sides. The two planes ABC and LOD intersect each other at the line segment AD or AD is the common line between the two planes. LOD is the far side of the cube. ABC is on the left side. So the intersection is the vertical EDGE AD, on the far left.
Therefore, the two planes ABC and LOD intersect each other at the segment AD.
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Let (8,−3) be a point on the terminal side of θ. Find the exact values of cosθ, cscθ, and tanθ.
Answer:
[tex]\text{Cos}\theta=\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{x}{R}=\frac{8}{\sqrt{73}}[/tex]
[tex]\text{Csc}\theta=-\frac{\sqrt{73}}{3}[/tex]
[tex]\text{tan}\theta =\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{y}{x}=\frac{-3}{8}[/tex]
Step-by-step explanation:
From the picture attached,
(8, -3) is a point on the terminal side of angle θ.
Therefore, distance 'R' from the origin will be,
R = [tex]\sqrt{x^{2}+y^{2}}[/tex]
R = [tex]\sqrt{8^{2}+(-3)^2}[/tex]
= [tex]\sqrt{64+9}[/tex]
= [tex]\sqrt{73}[/tex]
Therefore, Cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{x}{R}=\frac{8}{\sqrt{73}}[/tex]
Sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}=\frac{y}{R}=\frac{-3}{\sqrt{73} }[/tex]
tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{y}{x}=\frac{-3}{8}[/tex]
Cscθ = [tex]\frac{1}{\text{Sin}\theta}=\frac{R}{y}=-\frac{\sqrt{73}}{3}[/tex]
Part A) What is the cost of 14.6 gallons of gasoline at $2.70 per gallon? Part B) Explain the steps you would take to solve this problem.
Answer:
$39.42
Step-by-step explanation:
SImply multiply 14.6 with 2.70 which will give us 39.42.
Price:-
[tex]\\ \tt\hookrightarrow 14.6(2.7)[/tex]
[tex]\\ \tt\hookrightarrow 39.42\$[/tex]
Which set of ordered pairs could represent the same function as y = x2 ?
A (1, 1), (2, 4), (3,6)
B (1,1),(3,9), (7,49)
© (1,2), (4,16), (8, 64)
D (4,8), (5, 25), (6,36)
Answer:
B (1, 1),(3, 9), (7, 49)
Step-by-step explanation:
Given function:
y = x²Let's verify which set of pairs are same with the given function:
A....................
(1, 1) - yes(2, 4) - yes(3, 6) - no, 6≠ 3²B....................
(1, 1) - yes(3, 9) - yes(7, 49) - yesC....................
(1, 2)- no, 2≠ 1²(4, 16) - yes(8, 64) - yesD....................
(4, 8) - no, 8 ≠ 4²(5, 25) - yes(6, 36) - yes1. A research team wants to investigate the usefulness of relaxation training for reducing levels of anxiety in individuals experiencing stress. They identify 30 people at random from a group of 100 who have "high stress" jobs. The 30 people are divided into two groups. One group acts as the control group - they receive no training. The second group of 15 receive the relaxation training. The subjects in each group are then given an anxiety inventory. The summarized results appear below where higher scores indicate greater anxiety. Evaluate using the criteria of p < .05. Assume it is a two tailed test.
Answer:
a. H0:u1=u2
Ha:u1>u2
b. T-critical value =1.7011
c. We can conclude that relaxation training has reduced stress levels based on evidence gathered from statistical calculations
Step-by-step explanation:
Please find attachment
Flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet. What is the probability that a carpet that is 8 feet by 14 feet contains no flaws
Answer:
The probability that it contains no flaws=0.585
Step-by-step explanation:
Flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet.
One = 270 ft²
8*14= 112 ft²
Probability of containing flaws
So if 270 ft² = 1
112 ft² = 112/270
112ft² = 0.415
The probability that it contains no flaws= 1- probability that it contains
The probability that it contains no flaws= 1-0.415
The probability that it contains no flaws=0.585
What is the probability that a randomly chosen student admitted in the hospital is between 11 and 14 years
Answer:
convert 13.025 to base 10
What expression converts 100 inches per minute to feet per minute?
1 foot= 12 inches.
To convert you must have "2 fractions" to multiply.
Your first fraction must be 100in/1min. (100 inches per 1 minute).
The second should serve to convert inches to feet. It should be 1 foot/ 12 inches. (1 foot per 12 inches).
Your product should be 100ft/12 which equals 8.3 repeating or 25/3 (8 1/3) feet.
A company buys a machine for $225,000 that depreciates at a rate of 30% per year. Find a formula for the value of the machine after n years. V(n) =
Answer:
[tex]V(n) =225000*0.7^n[/tex]
Step-by-step explanation:
In this problem we are expected to model the depreciated value of the machine after some years of purchase (n years)
initial value of the machine is $225,000
after a year it reduces by 30%
Therefore the new value is now 70% of the initial value
[tex]= 225000*0.7= 157,500[/tex]
= $157,500
After another year it reduces by 30%
Hence the new value is
[tex]=225000*0.7^2\\\=225000*0.49\\\\\=110250[/tex]
= $110250
that after n years the value will be
[tex]V(n) =225000*0.7^n[/tex]
For i≥1 , let Xi∼G1/2 be distributed Geometrically with parameter 1/2 . Define Yn=1n−−√∑i=1n(Xi−2) Approximate P(−1≤Yn≤2) with large enough n .
Answer:
The answer is "0.68".
Step-by-step explanation:
Given value:
[tex]X_i \sim \frac{G_1}{2}[/tex]
[tex]E(X_i)=2 \\[/tex]
[tex]Var (X_i)= \frac{1- \frac{1}{2}}{(\frac{1}{2})^2}\\[/tex]
[tex]= \frac{ \frac{2-1}{2}}{\frac{1}{4}}\\\\= \frac{ \frac{1}{2}}{\frac{1}{4}}\\\\= \frac{1}{2} \times \frac{4}{1}\\\\= \frac{4}{2}\\\\=2[/tex]
Now we calculate the [tex]\bar X \sim N(2, \sqrt{\frac{2}{n}})\\[/tex]
[tex]\to \frac{\bar X - 2}{\sqrt{\frac{2}{n}}} \sim N(0, 1)\\[/tex]
[tex]\to \sum^n_{i=1} \frac{X_i - 2}{n} \times\sqrt{\frac{n}{2}}} \sim N(0, 1)\\\\\to \sum^n_{i=1} \frac{X_i - 2}{\sqrt{2n}} \sim N(0, 1)\\[/tex]
[tex]\to Z_n = \frac{1}{\sqrt{n}} \sum^n_{i=1} (X_i -2) \sim N(0, 2)\\[/tex]
[tex]\to P(-1 \leq X_n \leq 2) = P(Z_n \leq Z) -P(Z_n \leq -1) \\\\[/tex]
[tex]= 0.92 -0.24\\\\= 0.68[/tex]
On a tree farm, a forester wants to estimate the total number of trees with diameters exceeding 12 inches. A map of the farm is available. Discuss the problem of choosing appropriate sampling units and an appropriate frame.
Answer:
The problems associated with choosing appropriate sampling units and frame are given below;
Step-by-step explanation:
1. The only aid available to the forester or researcher is a map of the farm.
2. Appropriate sampling units will be hard to choose because farm trees are only characterized by attributes such as
- type of crop/plant (as all trees of a certain crop are much likely to have similar width or diameter)
- height of tree (as height is closely related to width)
- location of tree on the farm (e.g. North on the map, East on the map, South on the map, West on the map)
- age of tree (as older trees are more likely to have diameters exceeding 12 inches, than the younger trees)
- etcetera.
3. Appropriate frame (size) of sample will be hard to choose because a number of trees cannot just be selected from the total number of trees, if the categorization for sampling units is uncertain.
Select the correct answer.
Describe the solution to the system of equations graphed below.
The system has no solutions.
The system has infinitely many solutions of the form y = -x + 3, where x is any real number.
The system has a unique solution at (2,1).
O
The system has a unique solution at (1,2).
Answer:
answer is c
Step-by-step explanation:
i got it right
The solution of the system is unique and the solution is (2, 1). Then the correct option is C.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
If the two lines intersect, then the point of intersection represents the solution of the equations.
The solution of the system is unique and the solution is (2, 1).
The system has a unique solution at (2,1). Then the correct option is C.
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1. When bisecting a line segment, why must you find the intersection points of the arcs both above and below the line segment? A. To make sure that you get a straight line to bisect the line segment. B. The intersection point above the line segment overestimates the midpoint, while the intersection point below the line segment underestimates the midpoint. C. Finding both intersection points helps if the line segment is not completely vertical or horizontal. D. Only one intersection point is needed to find the midpoint, but finding both points allows you to check your work. 2. A line segment has a length of approximately 10 cm. If a compass is set to a width of 9 cm, will it still be possible to bisect the line segment? Explain. A. No, it is not possible. The compass should be just a little bit wider than half of the length of the line segment, which in this case is 5 cm. B. Yes, it is still possible. The width of the compass in respect to the length of the line segment does not matter. C. No, it is not possible. The width of the compass should be exactly half of the length of the line segment, which in this case is 5 cm. D. Yes, it is still possible. So long as the compass is wider than half the length of the line segment and still intersects the line segment, it is possible to bisect the line segment.
Answer:
A)Option A - To make sure that you get a straight line to bisect the line segment
B) Option D - Yes, it is still possible. So long as the compass is wider than half the length of the line segment and still intersects the line segment, it is possible to bisect the line segment.
Step-by-step explanation:
1) In bisection of a line segment, we seek to divide the line into 2 equal parts. Now, when using the bisection points of an arc, it's important to have two intersection points above and below the line segment so that we can draw a straight line that will pass through the horizontal line segment we are bisecting to make the bisected parts equal in length.
So option A is correct.
2) When bisecting a horizontal line segment using compass, usually we place one leg of the compass at one endpoint of the line and open the other leg of the compass to a length that's more than half of the horizontal line segment. Thereafter, we draw our arc from top to bottom. Without changing the distance of the opened compass, we put one of the legs at the 2nd endpoint and now draw another arc to intersect the previously drawn one.
Now, from the question we are told that the line segment has a length of approximately 10 cm and the compass is set to a width of 9 cm. Now, since 9cm is more than half of the line segment and provided this width of 9cm is maintained when moving the leg to the second endpoint, then it is possible.
Option D is correct.
Subtract.
Eight-ninths minus one-third
8/9 - 1/3
To subtract these two fractions, first find a common denominator.
The common denominator will be the
least common multiple for the two denominators.
In this case, the least common multiple of 9 and 3 is 9.
So to subtract, a denominator of 9 is needed in each fraction.
8/9 already has 9 in the denominator so it stays the same.
To get a 9 in the denominator of 1/3, multiply top and bottom by 3.
This gives us 3/9.
So we have 8/9 - 3/9 which is 5/9.
Answer:
Five-ninths
Step-by-step explanation:
Since the denominators are different (9 and 3) we need to change one of them.
9 is divisible by 3 therefor we do not need to change Eight-ninths.
3 times 3 = 9, nine becomes the new denominator, but remember, whatever we do to the bottom (denominator), we must also do to the top (numerator).
1 times 3 = 3
Now the equation is 8/9 - 3/9, we must only subtract the numerators. The answer is 5/9.
The amount of a chemical solution is measured to be 2 liters. What is the percent error of the measurement? 2.55% 25% 50%
Answer:
2.55 percent
Step-by-step explanation:
negative numbers are closed under addition True or False
What is the slope of the line?
A. −1/2
B. 2
C. −2
D. 1/2
Answer:
[tex]\frac{2}{1}[/tex]
Step-by-step explanation:
Hello!
To find the slope of a line we divide how many times it goes over by the number of times it goes up
The line goes over 4 and up 2 which is shown like
[tex]\frac{4}{2}[/tex]
We can simplify this
[tex]\frac{2}{1}[/tex]
The answer is [tex]\frac{2}{1}[/tex]
Hope this helps!
write a equation in a point-slope form fir the line through the given point with the given slope (9,-1);m=4/3
Answer:
y +1 = 4/3( x-9)
Step-by-step explanation:
Point slope form of an equation is
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on a line
y - -1 = 4/3( x-9)
y +1 = 4/3( x-9)
Describe the transformations from the graph of f(x)=∣x∣ to the graph of r(x)=∣x+2∣− 6.
The transformations are a horizontal translation 2 units right then a vertical translation 6 units down.
The transformations are a horizontal translation 2 units right then a vertical translation 6 units up.
The transformations are a horizontal translation 2 units left then a vertical translation 6 units down.
The transformations are a horizontal translation 2 units left then a vertical translation 6 units up.
Answer: The answer is C
The transformations are a horizontal translation 2 units left then a vertical translation 6 units down.
A company finds that the rate at which the quantity of a product that consumers demand changes with respect to price is given by the marginal-demand function Upper D prime (x )equals negative StartFraction 4000 Over x squared EndFraction where x is the price per unit, in dollars. Find the demand function if it is known that 1002 units of the product are demanded by consumers when the price is $4 per unit.
Answer:
D(x) = 4000 / x + 2
Step-by-step explanation:
Given:
marginal-demand function = d /dx[D(x )] = D'(x)= -4000/x²
Quantity of product demanded = 1002 units
Price of product per unit = $4
To find:
demand function D(x)
Solution:
D'(x)= -4000/x²
= -4000/x² dx
= -4000 x⁻² dx
D(x) = -4000 x⁻¹ + C
D(x) = -4000/x + C
Since we know that the quantity of product is 1002 and price per unit is $4 so,
D(4) = 1002 = 4000/4 + C
1002 = 4000/4 + C
1002 = 1000 + C
1002 - 1000 = C
C = 2
Hence the demand function is:
D(x) = 4000 / x + 2
Find the volume of the cylinder either enter an exact answer in terms of pi or use 3.14 for pi
1/2πr^2h.
1/2×3.142×3^2×2=
1/2×56.556=28.278~ 28.
Answer:
18pi
Step-by-step explanation:
I just got it right on Khan Academy
Alec makes jam to sell at a local farmers' market. To make last week's batch, he used 2 cups of sugar and 18 cups of berries. It was so popular that he made a larger batch this week. To make this week's batch, Alec used 4 cups of sugar and 30 cups of berries, and the jam sold out even faster. Which batch had a greater ratio of sugar to berries?
Answer:
This week's batch had the greater ratio of sugar to berries
Step-by-step explanation:
Last week's ratio was 2:18
This week's ratio was 4:30
Now, we can simplify both of these:
Divide last week's by 2:
1:9
Divide this week's by 2:
2:15
1:9 is equivalent to 0.11, and 2:15 is equivalent to 0.13
So, this week's batch had the greater ratio of sugar to berries
The batch with 4 cups of sugar and 30 cups of berries has a greater ratio of sugar to berries and is given by the proportion B = 4/30 = 0.1333
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion equation be represented as A and B
Now , for the last week's batch
Alec used 2 cups of sugar and 18 cups of berries
So , the ratio of sugar to berries is 2 : 18
The proportion is 2 / 18 = 0.1111
Now , for this week's batch
Alec used 4 cups of sugar and 30 cups of berries
So , the ratio of sugar to berries is 4 : 30
So , the proportion is 4 / 30 = 0.1333
Now , the proportion of 4 : 30 is greater than 2 : 18
Hence , this week's batch had a greater proportion
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Plz help 7th grade math ASAP
A bicycle has a listed price of $871.95 before tax. If the sales tax rate is 6.25%, find the total cost of the bicycle with sales tax included. Round your answer to the nearest cent, as necessary.
Answer:
$926.45
Step-by-step explanation:
$871.95 x .0625 = $54.50
$871.95 + $54.50 = $926.45
Answer:
$926.44
Step-by-step explanation:
sales tax = price*sales tax rate
sales tax = $54.49
871.95+54.49 = answer I think
Find the area of a triangle whose vertices are P(1,3,2) Q(2,-1, 1) R(-1,2,3)
Answer:
5199
Step-by-step explanation:
Because
36,815 to the nearest hundred
Answer:
36,800
Step-by-step explanation:
If x < 5, we round down.
If x ≥ 5, we round up.
We are specifically looking at 8 and 1 in 36,815.
1 < 5, so we round down:
36,800
how many lines are symmetry has an isosceles triangle
Which of the following is a monomial ? 9/x 11x2 20x9-7x 20x -14
Answer: 11x^2
Step-by-step explanation:
I suppose that the options are:
a) 9/x
b) 11x^2
c) 20x^9-7x
d) 20x -14
First, a polynomial is something like:
aₙx^n + .... + a₂*x^2 + a₁*x^1 + a₀*x^0
Where n is the degree of the polynomial, the therms a are the coefficients, and aₙ is the leading coefficient.
Depending on the number of terms of the polynomial, it takes different names.
If we have only one term, it is called a monomial, if it has two terms, it is called a binomial, and so on.
So if we want to find a monomial, then we need to look at the options with only one term.
The options with only one term are options a and b.
But option a is a quotient (we have a negative power of x: 9/x = 9*x^-1)
So this is not a polynomial, then the correct option is option b.