When drawing one card from a deck of 52 cards, the probability of obtaining either a spade or an ace are 4/13.
Given,
Number of cards in a deck = 52
Number of spades = 13
Number of aces = 4
Number of ace of spade = 1
We have to find the probability of getting either a spade or an ace when drawing a single card from the deck;
Here,
Probability of either a spade or an ace :
P(spade or ace) = P(spade U ace)
P(spade U ace) = p(spade) + p(ace) - p(spade n ace)
Now,
Probability = required outcome / Total possible outcomes
P(spade) = 13 / 52
P(ace) = 4 / 52
P(spade n ace) = 1 / 52
Then,
P(spade U ace) = p(spade) + p(ace) - p(spade n ace)
= 13/52 + 4/52 - 1/52
= 16 / 52 = 4 /13
That is,
The probability of getting either a spade or an ace when drawing a single card from a deck of 52 cards is 4/13
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An object weighing 5 pounds on Earth will weigh 2 pounds on Mercury. The Statue of Liberty weighs 225 tons. What would it weigh on Mercury? Show all work:
Answer:
90 tons
Step-by-step explanation:
given that the ration of weight from earth to mercury is 5:2, we can make an equation:
x (weight of an item on Mercury) = 0.4(weight of an item on Earth)
x=0.4(225 tons)
x=90 tons
Using the diagram of a regular hexagon, fill in the blanks for the steps to solve for the area of a hexagon with sides equal to 12 cm.
(1) How many equilateral triangles are there? _____
(2) What is the measure of each of the three angles in the equilateral triangle? _____
(3) If we cut an equilateral triangle down the middle (segment a), what special right triangle do you create? _____
(4) What is the vocabulary word for the segment a? _____
(5) What is the length of the short side of one of the 30-60-90 triangles? _____
(6) What is the length of the hypotenuse of one of the 30-60-90 triangles? _____
(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg of one of the 30-60-90 triangles. _____
(8) What is the height of one of the the equilateral triangles? _____
(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. _____
(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _____
The blanks are shown below for the area of hexagon with sides equal to 12cm.
What is Hexagon?In geometry, a hexagon is defined as a six-sided polygon. The two-dimensional form contains six sides, six vertices, and six angles.
All of the fill in the blanks are answered below:
(1) The number of equilateral triangles are 6
(2) The measure of each of the three angles in the equilateral triangle 60°
(3) If we cut an equilateral triangle down the middle the special right triangle we create is 30-60-90
(4) The vocabulary word for the green line is perpendicular bisector.
(5) The length of the short side of one 30-60-90 triangle is 4cm
(6) What is the length of the hypotenuse of one 30-60-90 triangle is 8cm
(7) Using the properties of 30-60-90 triangles, the length of the long leg. is 4√3cm
(8) The height of the equilateral triangle is 4√3cm
(9) The area of one equilateral triangle is ½(8)(4√3) = 16√3 cm²
(10) The area of one equilateral triangle by the number of triangles. is 8(16√3) = 128√3 cm²
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the product of two positive integers is 18. the positive difference of these two integers is 3. what is the sum of the two integers?
The sum of the given two positive integers is 9.
According to the question,
We have the following information:
The product of two positive integers is 18. the positive difference of these two integers is 3.
Now, let's take the first positive integer (larger one) to be x and the second positive integer to be y.
xy = 18 ...(1)
x-y = 3
x = 3+y
Putting this value in equation 1:
(3+y)y = 18
[tex]y^{2} +3y-18 = 0[/tex]
[tex]y^{2}[/tex]+6y-3y-18 = 0
y(y+6)-3(y+6) = 0
(y+6) (y-3) = 0
y-3 = 0 and y+6 = 0
y = 3 or y = -6
Now, the number is positive so it will be 3.
Putting this value in equation 1:
xy = 18
3x = 18
Dividing by 3 on both sides of the equation:
x= 18/3
x = 6
Sum of integers = 3+6
Sum of integers = 9
Hence, the sum of the given two positive integers is 9.
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a right triangle has a hypotenuse of length 3 units and one side of length 2 units. what is the area of the triangle?
The area of the triangle is 3 units^2. Since the area is equal to
hside * side/ 2.
Define area.
The measure of a region's size on a plane or curved surface is called area. While surface area refers to the area of an open surface or the boundary of a three-dimensional object, the area of a plane region or plane area refers to the area of a form or planar lamina.
Area is defined as the total amount of space occupied by a flat (2-D) surface or the shape of an object. On a sheet of paper, draw a square with a pencil. It is a two-dimensional figure. The area of a shape on paper is the area it occupies.
Solution Explained:
Given,
Length of Hypotenuse = 3units
One side = 2units
Area = (Length of Hypotenuse X Length one side) / 2
= (3 X 2) / 2
= 3units^2 (after calculation)
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Jill and Norachai are selling pies for a school fundraiser. Customers can buy cherry pies and pumpkin pies. Jill sold 8 cherry pies and 1 pumpkin pie for a total of $42. Norachai sold 6 cherry pies and 1 pumpkin pie for a total of $34. Find the cost each of one cherry pie and one pumpkin pie.
Answer:Cherry is $4 and Pumpkin is $10
Step-by-step explanation:
Answer:
Cherry Pie: $5 each
Pumpkin Pie: $2 each
Hope this helps! :)
Step-by-step explanation:
Jill- $42, 1 Pumpkin, 8 Cherry
8*5=40
Cherry: $5 each
42-40=2
Pumpkin: $2 each
Norachai- $32, 1 Pumpkin, 6 Cherry
6*5=30
Cherry: $5 each
32-30=2
Pumpkin: $2 each
Someone pleasee helppp!
Geometry A
Answer: I think it is 5
Step-by-step explanation:
Baldwin bought 4.2 pounds of melon and 4.44 pounds of cherries. How much fruit did he buy in all?
Answer: 8.64
Step-by-step explanation:
If you add 4.44 and 4.2 you would get 8.64 pounds worth of fruits in total.
Answer:
8.64 pounds of fruit.
Step-by-step explanation:
4.2 + 4.44 = 8.64 pound of fruit
8x - 4y = -4 solve for y.
The equation 8x - 4y = -4 have y as the subject to be equal to 2x + 1 expresses in terms of x.
How to evaluate for yTo solve for y in the equation 8x - 4y = -4, we must make y the subject and it should be positive as follows;
8x - 4y = -4
add 4y to both sides
8x - 4y + 4y= -4 + 4y
8x = - 4 + 4y
also to make y the subject;
- 4 + 4y = 8x
add 4 to both sides
- 4 + 4 + 4y = 8x + 4
4y = 8x + 4
factorize the right hand side
4y = 4(2x + 1)
divide through by the coefficient of y
4y/4 = [4(2x + 1)]/4
y = 2x + 1
Hence, the equation 8x - 4y = -4 has y = 2x + 1
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read the first five results and summarize the models they describe. choose one you find interesting, and determine how it is similar to the nist sp 800-100 model. how is it different?
Answer: Both the National Institute of Standards and Technology (NIST)
Step-by-step explanation:
a trough is 12 feet long and 3 feet across the top (see figure). its ends are isosceles triangles with altitudes of 3 feet. if water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising (in feet per minute) when \displaystyle hh is 1 foot deep?
If water is being pumped into the trough at 2 cubic feet per minute, then the water level rising (in feet per minute) when h is 1.6 foot deep is 0.1 feet cubic per minute.
Suppose that we have a function y = f(x), and wish to find the rate of change of y with respect to a third variable t, where we do not have y expressed explicitly in terms of t. We use the chain rule in differentiation to find this rate of change in a process called implicit differentiation.
dy/dt = dy/dx × dx/dt
If base is equal to the height, by similar triangles:
Volume v = base x height x length/2
= bhl/2
= h²12/2
= 6h².
Therefore,
dv/dt = 12hdh/dt
= 2 ft³/min
Now,
dh/dt = 2/(12h)
when h = 1.6,
dh/dt = 2/(12 × 1.6) ≈ 0.1 ft³/min
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The distance from the floor of one level of a building to the floor of the level above it is 9 feet 3/8 inches. If the distance from the floor to the ceiling is 8 feet 2 5/8 inches, how thick is the space between the ceiling of the one floor and the floor of the level above it?
The space between the ceiling of the one floor and the floor of the level above it will be;
⇒ 9 6/8 inches
What is mean by Subtraction?
Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The distance from the floor of one level of a building to the floor of the level above it is 9 feet 3/8 inches.
And, The distance from the floor to the ceiling is 8 feet 2 5/8 inches.
Now,
Since, The distance from the floor of one level of a building to the floor of the level above it is 9 feet 3/8 inches.
And, The distance from the floor to the ceiling is 8 feet 2 5/8 inches.
Hence, The space between the ceiling of the one floor and the floor of the level above it will be;
⇒ 9 feet 3/8 inches - 8 feet 2 5/8 inches
⇒ (9 × 12 + 3/8) inches - ( 8 × 12 + 21/8) inches
⇒ (108 + 3/8) - (96 + 21/8) inches
⇒ 867/8 - 789/8
⇒ 78/8
⇒ 9 6/8 inches
Thus, The space between the ceiling of the one floor and the floor of the level above it will be;
⇒ 9 6/8 inches
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why in models such as logistic regression we need to estimate the marginal effects of each independent variable in order to understand how a change in one independent variable affects our dependent variable.
In a simple linear regression model , if we change the input variable by 1 unit , output variable will change by its slope.
What is linear regression?
According on the value of another variable, a variable's value can be predicted using a linear regression analysis. The dependent variable is the one you're trying to forecast. The term "independent variable" refers to the variable you are using to forecast the value of the other variable.
For linear regression
Y=a + bx + error
If we neglect error
then Y=a + bx.
If x increases by 1
then Y = a +b(x+1) which implies
Y=a + bx + b.
So Y increases by its slope.
Hence their is an increase in the slope in y.
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How many numbers in the range 1000 - 9999 have no
repeated digits?
Answer:4536 numbers.
Step-by-step explanation:
Since 1 st digit cannot be zero the first digit can be anything from 1–9 ( total 9)
The second digit ( any 10- 1 above)
The third digit ( any 10–2 above)
The last digit ( any 10–3 above)
Total 9x9x8x7 =
4536
:)
The graph shows the relationship between time and the number of soda bottles a machine can make. Use the points (3,48) and (7,112) to find the number of soda bottles the machine can make each minute.
The number of soda bottles the machine can make in each minute is 960 bottles
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the number of soda bottles the machine can make in 1 minute be = y
Now , the equation is
Let the first point in the graph be A ( x₁ , y₁ )
The value of A ( x₁ , y₁ ) = A ( 3 , 48 )
Let the second point in the graph be B ( x₂ , y₂ )
The value of B ( x₂ , y₂ ) = A ( 7 , 112 )
Now , the slope of the line joining the points can be found out from the equation of slope
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
So , the slope of the point is m = steep of the line or inclination
Slope m = y / x
Substituting the values for x and y , we get
Slope m = 48 / 3
Slope m = 16
Therefore , the equation of line will be y = mx + c
y = 16x
Now , there are 60 seconds in a minute
So , 1 minute = 60 seconds
Substituting the value of x = 60 in the equation , we get
y = 16x
y = 16 x 60
y = 960 bottles
Therefore , the value of y = 960
Hence , The number of soda bottles the machine can make in each minute is 960 bottles
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PLEASE HELP ME IM GROUNDED AND MY TRIMESTER ENDS TONIGHT
Answer:
Step-by-step explanation:
Set angle equations equal to each other(since lines are parallel)
7x-4= 5x+10
Add 4 to both sides to isolate x on left side
7x= 5x+14
Subtract 5x from both sides to get x on one side only.
2x=14
x=7
5. the chi-square test for goodness of fit - no difference from a known population suppose you are reading a study conducted in the year 2000 about welfare recipients in the united states. the authors report the following frequency data on the household size of the 1,844 welfare recipients in their random sample: observed frequencies household size 5-or-more-person 4-person 3-person 2-person 1-person 203 277 301 550 513 you wonder if welfare recipients tend to live in different-sized households than the us population at large. you obtain the following data from the 2000 census: percent distribution of us households by size household size 5-or-more-person 4-person 3-person 2-person 1-person 10.83% 14.20% 16.53% 32.63% 25.81% [source: hobbs f., & Stoops, N. (2002). Census 2000 special reports: Demographic trends in [Source: the 20th century. U.S. Census Bureau.] You use a chi-square test for goodness of fit to see how well the sample of welfare recipients fits the census data. What is the most appropriate null hypothesis? O The distribution of household sizes among welfare recipients is the same as that provided by the census data. The distribution of household sizes among welfare recipients is equal across the five household-size categories. O The distribution of household sizes among welfare recipients is different from that provided by the census data. O The distribution of household sizes among welfare recipients is not equal across the five household-size categories. Fill in the missing values in the following table indicating the expected frequencies in each category for a sample size of 1,844, if the null hypothesis is true: Expected Frequencies Household Size 5-or-more-person 4-person 3-person 2-person 1-person 475.94 304.81 601.70 The chi-square statistic has been calculated for you: x2 = 8.31. The distribution of the chi-square statistic has degrees of freedom. Use the following Distributions tool to find the critical value. Chi-Square Distribution Degrees of Freedom = 4 4 10 11 12 13 14 With the level of significance a = .01, the critical value is Because the chi-square statistic x2 is the critical value, you the null hypothesis. Therefore, you conclude that the proportions of welfare recipients in the five household-size categories differ from the corresponding proportions for all U.S. households.
The confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17
On Subtracting 1 from your sample size, we get
150 – 1 = 149.
On Subtracting confidence level from 1, and then divide by two.
(1 – .95) / 2 = 0.025
Now, df = 149 and α = 0.025
from the table at df = 149 we got 2.262.
Divide your sample standard deviation by the square root of your sample size.
28 / √(150) = 2.28
Now, 2.262 × 2.28 = 5.17
So, the confidence interval be,
(150 - 5.17 , 150 + 5.17) = (144.83 , 155.17)
Hence, the confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17
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4. demonstrate whether the data support the hypothesis that the xanthan gum solutions are pseudoplastic?
Because xanthan gum solutions are highly pseudoplastic (shear thinning) but not thixotropic, the initial viscosity is instantly rebuilt after high shearing.
What is hypothesis?A hypothesis is a theory put up to explain a phenomena. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are often based on prior findings that cannot be adequately explained by the current body of knowledge. A hypothesis is a statement that makes sense in light of the available information but hasn't been proved true or wrong. A hypothesis in statistics is a claim that will serve as the foundation for hypothesis testing (also known as a statistical hypothesis).
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How many solutions does this equation have? –2g + 2g = 0
The equation -2g+2g has infinitely many solutions.
Define solving an equation.The method of solving equations involves determining the value of the unknown variable while maintaining the equality of the equation on both sides. When a condition on variable guarantees that two expressions in the variable have the same value, it qualifies as an equation. The equation's solution is the value of the variable for which the equation is true. An equation remains the same even when the LHS and RHS are flipped. After separating the variable whose value has to be calculated, the solution is found. We can answer it depending on the type of equation we are dealing with. Equations come in a variety of forms, including linear, quadratic, rational, and radical equations.
Consider the given equation
-2g + 2g = 0
Solve the equation,
0 = 0
This means that the equation is valid for all values of g.
Therefore, the equation can have infinitely many solutions.
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phenolphthalein has a pka of 9.7 and is colorless in its acid form and pink in its basic form. for ph= 5.3 calculate [in−]/[hin] . for ph= 11.4 calculate [in−]/[hin] .
Part a: [In⁻]/[HIn] = 4.0 × 10⁻⁶
Part b: [In⁻]/[HIn] = 50.11, for the given phenolphthalein solution.
Explain the term acid form?Typical aqueous acids include acetic acid, hydrochloric acid, and gastric acid, which activates digestive enzymes. Hydrochloric acid is a solution containing hydrogen chloride.Using the Henderson-Hasselbalch equation to determine the indicator's pH is as follows:
pH = pKa + log[In⁻]/[HIn]
In which,
Ka = dissociation constant of acid.
As the stated value-
Part a:
pKa = 9.7
pH = 5.3
Thus,
5.3 = 9.7 + log[In⁻]/[HIn]
log[In⁻]/[HIn] = - 4.4
[In⁻]/[HIn] = Antilog (-4.4)
[In⁻]/[HIn] = 4.0 × 10⁻⁶
Part b:
pKa = 9.7
pH = 11.4
Thus,
11.4 = 9.7 + log[In⁻]/[HIn]
log[In⁻]/[HIn] = 1.7
[In⁻]/[HIn] = Antilog (-4.4)
[In⁻]/[HIn] = 50.11
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kennedy needs to order some new supplies for the restaurant where she works. the restaurant needs at least 512 spoons. there are currently 264 spoons. of each set on sale contains 6 spoons, what is the minimum number of sets of spoons kennedy should buy?
Kennedy needs purchase at least 42 sets of spoons.
Explain the term inequality of numbers?An algebraic expression with two values that are not equal is represented by an inequality. A sign of inequality can be used to show that one of the two variables is larger than, greater than or comparable to, less than, or equal to another value.The minimum set of spoons needed in the restaurant = 512 spoons.
Available spoons = 264.
Each set on the sale has 6 spoons.
Let the minimum number of spoon set required be 'x'.
Then,
6x + 264 ≥ 512
Solving the in equality.
6x ≥ 512 - 264
6x ≥ 248
x ≥ 248/6
x ≥ 41.33
Thus, Kennedy needs purchase at least 42 sets of spoons.
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an office typically orders 60 ink refills at a time. the company estimates that handling costs are 40% of the $10 unit cost and the monthly demand is around 20 units. the assumptions of the basic eoq model are applicable. what would be the cost to order?
Cost to order as per the economic order quantity model is equal to 10units.
As given in the question,
Demand of units per month = 20 units
Ordering cost = $10 unit
Carrying cost = 40% of 10
= (40 /100) × 10
= $4
Economic order quantity model ( EOQ)
= √[ 2 × ( Demand rate ) × ordering cost ]/ carrying cost
Substitute the value we get,
= √ ( 2 × 20 × 10 )/ 4
= √400 / 4
= √100
= 10 units.
Therefore , as per the economic order quantity (EOQ) model cost to order is for 10 units.
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a group of n people plays a game. each person puts their name on a slip of paper in a hat, and then picks a name randomly from the hat (without replacement). what is the standard ceviation of the number x of people who pick their own name (assume n≥2)?
Given that each individual has a [tex]\frac{1}{n}[/tex] chance of receiving their own name, we may indicate whether or not person I received their own name by using a sequence of n identically distributed Bernoulli random variables with
[tex]P=\frac{1}{n}[/tex] .
The total number of people who received their own name is the sum of these Bernoullis. The linearity of expectation causes the expected value of the sum to equal the sum of their respective expected values.
Since each summand has expected value [tex]\frac{1}{n}[/tex] and there are n of them, the expected value is one.
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Graph each function and identify its domain, range, intercepts, asymptotes, and holes.
Thank you! :)
Answer: The domain is : (-∞,5)∪(5,∞)
there is no x intercepts
y-intercept= (0,-29/5)
asymptotes= x=5, no horizantal, oblique y=x-5
there is no holes
range= (-∞,-4]∪[4,∞)
Step-by-step explanation:
Study the pattern in the table. Tell whether the relationship between x and y is linear, exponential, or neither, and explain your answer. If the relationship is linear or
exponential, write an equation for it.
a group of 15 people are ordering pizza each person wants 2 slices and each pizza has 15 slices how many pizzas should they buy
By conducting mathematical operations, we know that the group of friends will order 6 pizzas.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.
The operation's arity is determined by the number of operands.
Mathematical operations include addition, subtraction, multiplication, division, and finding the root.
So, a number of pizzas the friends should buy:
We know that a group is of 15 people.
They are ordering a pizza which have also 15 slices in each.
And each person wants 2 slices: That is
Then, the number of pizzas they have to order will be:
1 pizza (15 slices) * 2 = 2 pizza (30 slices)
Therefore, by conducting mathematical operations, we know that the group of friends will order 6 pizzas.
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use the appropriate normal distribution to approximate the resulting binomial distributions. a fair coin is tossed 130 times. what is the probability of obtaining between 55 and 69 tails, inclusive? a) 0.7523 b) 0.7134 c) 0.7221 d) 0.7179 e) 0.7494 f) none of the above.
The probability is 0.6962 for the given standard deviation.
What is standard deviation?
Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.
Main body:
X - Binomial(n = 130, p = 0.5)
Binomial can be approximated to normal with: μ = np = 130*0.5 = 65
σ = √np(1 − p) - = √130* (0.5)(1 − 0.5)
σ = 5.7
P(55 ≤ X ≤ 69 )
Since we are approximating a discrete binomial distribution by continuous normal distribution, values between 54.5 and 68.5 both approximate to 55. Thus, "between 55 and 69" corresponds to continuous normal distribution with P(54.5 < X 68.5) after continuity correction.
Normal Distribution, x₁ = 54.5, x2 = 68.5, µ = 65, σ = 5.7
We convert this to standard normal using z =
z₁ = 54.5-65/ 5.7 ≈ - 1.84
z₂ = 68.5-65/ 5.7 ≈ 0.614
P(54.5 < X < 68.5) = P(- 1.84 < Z < 0.614)
= P(Z < 0.614) − P(Z <- 1.84)
= 0.7291 - 0.0329 (from z-table)
= 0.6962
Hence the probability is 0.6962
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Solve for all values of c in simplest form
19 = | 5c - 4 |
The values of c in the given equation, 19 = | 5c - 4 |, are c = -3 and c = 4 3/5
Solving an equationFrom the question, we are to solve the given equation for all values of c
The given equation is
19 = | 5c - 4 |
From this equation, we can write that
19 = (5c - 4) and 19 = -(5c - 4)
Solving the first equation
19 = (5c - 4)
19 = 5c - 4
Add 4 to both sides of the equation
19 + 4 = 5c - 4 + 4
23 = 5c
Divide both sides by 5
23/5 = 5c/5
4 3/5 = c
Therefore,
c = 4 3/5
Solving the second equation
19 = -(5c - 4)
19 = -5c + 4
Subtract 4 from both sides of the equation
19 - 4 = -5c + 4 - 4
15 = -5c
Divide both sides by -5
15/-5 = -5c/-5
-3 = c
Therefore,
c = -3
Hence, the values of c are -3 and 4 3/5
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Tiyanna works at a car dealership. When she sells a car, she earns a $1,400 commission and the dealership earns $33,600. At this rate, how much commission would Tiyanna earn if she sells a car for $42,000?
Answer: $1,751.4
Step-by-step explanation:
33600 = 100%
(1400*100)/33600 =
140000:33600 = 4.17
42,000 * 4.17% = 1,751.4
What are advantages and disadvanteges when using percent to measure change?
Answer:
Step-by-step explanation:
Percentages are a powerful way to compare samples with different numbers of observations. By standardising measures using a scale of 0 to 100, samples can be compared quickly and easily. Any graph of the data, however, must include the full range of 0 to 100 to ensure that false impressions are not created.
Maria's plant grew 3 1/4 inches every month for 2 1/2 months. How many inches did Maria's plant grow during that time?
Answer: 8.125 inches
Step-by-step explanation: Ok so if the plant grew 3.25 inches every month, and there were 2.5 months, you need to multiply 3.25 by 2.5 to get the total amount of growth. So that would be 8.125.
Hope that helped!