21.Bill and Sam are playing a game where they roll a die and draw a card from a deck. What is the probability of rolling a 5 and then drawing a 5 from the deck of cards? Write your answer as a fraction in lowest terms.
Answers
So we must find the probability that two independent events happen at once. These events are rolling a 5 and drawing a 5 from the deck. Since they are independent events because the result of one of them doesn't depend on the result of the other the probability that both happen is given by the product of their individual probabilities.
The probability of rolling a 5 is given by the quotient between the number of 5's in the die and the total number of faces in the die. There's only one 5 in the die and it has 6 faces so the probability of rolling a 5 is:
\(P(r5)=\frac{1}{6}\)A standard deck has 52 cards and four of those cards are fives. Then the probability of drawing a 5 is given by the quotient between the number of fives in the deck and the total number of cards in it. Then we get:
\(P(d5)=\frac{4}{52}=\frac{1}{13}\)Then the probability of rolling a 5 and then drawing a 5 from the deck is given by the product of the two probabilities that we found before:
\(P=\frac{1}{6}\cdot\frac{1}{13}=\frac{1}{78}\)AnswerThen the answer is 1/78.
Related Questions
A 5-pound bag of apples cost $3.50. Use that rate, to complete the table to identify equivalent ratios, and then answer the questions.
Apples *? 5 ? 15
Cost 0.70 3.50 7 *?
Answers
choose the x-intercept and y-intercept of the equation 6x-y=7a (0,-7)b (0,7)c (6/7,0)d (7/6,-7)e (7/6,0)
Answers
Given:
\(6x-y=7\)Find-: X-intercept and Y-intercept of the equation.
Sol:
For X-intercept value of "y" is zero.
\(\begin{gathered} 6x-y=7 \\ \\ y=0 \end{gathered}\)So, the x-intercept is:
\(\begin{gathered} 6x-y=7 \\ \\ y=0 \\ \\ 6x-0=7 \\ \\ 6x=7 \\ \\ x=\frac{7}{6} \end{gathered}\)The x-intercept is 7/6.
The Y-intercept of the equation then the value of "x" is zero.
\(\begin{gathered} 6x-y=7 \\ \\ x=0 \end{gathered}\)So, the y-intercept is:
\(\begin{gathered} 6x-y=7 \\ \\ x=0 \\ \\ 6(0)-y=7 \\ \\ 0-y=7 \\ \\ y=-7 \end{gathered}\)So, the y-intercept is -7.
\((x-\text{ intercept, }y-\text{ intercept\rparen = \lparen}\frac{7}{6},-7)\)find the values of the variables in the matrix calculator
Answers
Double-check the input and review the solution provided by the matrix calculator to ensure accuracy.
The matrix calculator is a useful tool for solving equations involving matrices. To find the values of the variables in the matrix calculator, follow these steps:
1. Enter the coefficients of the variables and the constant terms into the calculator. For example, if you have the equation 2x + 3y = 10, enter the coefficients 2 and 3, and the constant term 10.
2. Select the appropriate operations for solving the equation. The calculator will provide options such as Gaussian elimination, inverse matrix, or Cramer's rule. Choose the method that suits your equation.
3. Perform the selected operation to solve the equation. The calculator will display the values of the variables based on the solution method. For instance, Gaussian elimination will show the values of x and y.
4. Check the solution for consistency. Substitute the obtained values back into the original equation to ensure they satisfy the equation. If they do, you have found the correct values of the variables.Remember to double-check the input and review the solution provided by the matrix calculator to ensure accuracy.
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"Consider the following function: f(x,y)=y^5 ln(−2x^4+3y^5) find fx and fy"
Answers
From the function f(x,y)=y⁵ ln(−2x⁴+3y⁵). The value of fx = -10x³y⁵ / (-2x⁴ + 3y⁵) and
fy = y⁴ * ln(-2x⁴ + 3y⁵) * d/dy [(-2x⁴ + 3y⁵)]
To find fx, we differentiate f(x,y) with respect to x, treating y as a constant:
fx = d/dx [y⁵ ln(-2x⁴ + 3y⁵)]
Using the chain rule and the derivative of ln u = 1/u, we have:
fx = y⁵ * 1/(-2x⁴ + 3y⁵) * d/dx [-2x⁴ + 3y⁵]
Simplifying and applying the power rule of differentiation, we get:
fx = -10x³y⁵ / (-2x⁴ + 3y⁵)
Similarly, to find fy, we differentiate f(x,y) with respect to y, treating x as a constant:
fy = d/dy [y⁵ ln(-2x⁴ + 3y⁵)]
Using the chain rule and the derivative of ln u = 1/u, we have:
fy = y⁴ * ln(-2x⁴ + 3y⁵) * d/dy [(-2x⁴ + 3y⁵)]
Applying the power rule of differentiation and simplifying, we get:
fy = 15y⁴ ln(-2x⁴ + 3y⁵)
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Jonah bought 3 packages of hot dogs and 2 packages of hot dog buns and paid $21.90. He went back and purchased 2 more packages of hot dogs and 5 more packages of hot dog buns and paid $23.40. ASSUMMING THERE WAS NO CHANGE IN THE INDIVIDUAL COST OF EACH ITEM:
What is the cost per package of hot dogs and hot dog buns?
IT IS NOT $7.30 AND $3.65!!!
Answers
Answer:
b = $2.40
d = $5.70
Step-by-step explanation:
d = hot dog and b = hot dog buns
Equations:
2d + 5b = $23.40
3d + 2b = $21.90
-------------------------------subtract these two equations
-d + 3b = $1.50
3b - $1.50 = d
Substitute:
3d + 2b = $21.90
3(3b - $1.50) + 2b = $21.90
9b - $4.50 + 2= $21.90
11b = 26.40
b = $2.40
Substitute again but this time with b:
3d + 2b = $21.90
3d + 2($2.40) = $21.90
3d + $4.80 = $21.90
3d = $21.90
d = $5.70
A gardening store ordered 222,840 potted plants last year. This year, the store ordered 5% more than that number. How many potted plants were ordered this year?
Answers
Answer:
233982
Step-by-step explanation:
Answer:
233,982
Step-by-step explanation:
222840x0.05=11142
222840+11,142= 233,982
a guy wire runs from the top of a cell tower to a metal stake in the ground. rashon places a 6-foot tall pole to support the guy wire. after placing the pole, rashon measures the distance from the stake to the pole to be 4 ft. he then measures the distance from the pole to the tower to be 9 ft. find the length of the guy wire, to the nearest foot.
Answers
The length of the guy wire, to the nearest foot is 23 feet.
How to calculate the length of the guy wire?Based on the information provided, we can logically deduce that triangle ABE (ΔABE) is similar to triangle (ΔCDE) and the following parameters about the geometric figures;
CD = 6 ft.DE = 4 ft.BD = 9 ft.Additionally, the corresponding sides of similar triangles are equal;
AB/CD = BE/DE
AB/6 = (9 + 4)/4
AB/6 = 13/4
AB = 19.5 feet.
By applying Pythagorean' theorem, side AE is given by:
AE = √(AB² + BE²)
AE = √(19.5² + 13²)
AE = 23.44 ≈ 23 feet.
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In the later afternoon on a sunny day, Shanice goes outside with a tape measure. She first measures her shadow which is 7 feet 6 inches long. She then measures the shadow of the oak tree in the back yard which is a whopping 74 feet 3 inches. Not content to stop there, she also measures the shadow of her house (taking the longest measurement possible) and finds that it is 28 feet 6 inches. Using this information, find out how much taller the tree is than the house if Shanice's actual height is 5 feet 10 inches.
Answers
Answer:
29 feets 3 inches
Step-by-step explanation:
We need to obtain the actual height of oak tree :
Converting measurement to inches :.
1 Feet = 12 inches
Shanice height, SA = 5ft 10 in = (12*5 + 10) = 70 in
Shanice shadow, SS = 7ft 6in = (12*7 + 6) = 90 in
Tree shadow, TS = 74ft 3 in =(12*74 + 3) = 891 in
Let actual tree height = TH
Using the relation :
SA / SS = TH / TS
70 / 90 = TH / 891
Cross multiply :
90 * TH = 891 * 70
TH = (891 * 70) / 90
TH = 693 inches
Height of house = 28ft 6 in = (28*12 + 6) = 342 in
Height difference :
(693 - 342) in = 351 inches
351 in / 12 = 29 feets 3 inches
in 250 explain the power of substitutes from porters 5
forces
Answers
The power of substitutes is one of the five forces in Porter's Five Forces framework and it is a measure of how easy it is for customers to switch to alternative products or services. The higher the power of substitutes, the more competitive the industry and the lower the profitability.
The power of substitutes is based on the premise that when there are readily available alternatives to a product or service, customers can easily switch to those alternatives if they offer better value or meet their needs more effectively. This poses a threat to the industry as it reduces customer loyalty and puts pressure on pricing and differentiation strategies.
The availability and quality of substitutes influence the degree to which customers are likely to switch. If substitutes are abundant and offer comparable or superior features, the power of substitutes is strong, increasing the competitive intensity within the industry. On the other hand, if substitutes are limited or inferior, the power of substitutes is weak, providing more stability and protection to the industry.
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Find the slope of the tangent line to the curve 4 sin(x) + 6 cos(y) – 4 sin(x) cos(y) + x = 41 at the point (47,57/2).
Answers
At the point (47,57/2) on the curve 4 sin(x) + 6 cos(y) - 4 sin(x) cos(y) + x = 41, the slope of the tangent line is about 1.607. Finding the partial derivatives with respect to x and y, evaluating them at the given position, and obtaining their ratio results in the calculation of this.
The partial derivatives with regard to x and y must be discovered, evaluated at the given position, and then used to determine the slope of the tangent line to the curve 4 sin(x) + 6 cos(y) - 4 sin(x) cos(y) + x = 41.
Taking the partial derivative of the equation with respect to x, we obtain:
(4) cos(x) - (4) cos(y) + (1) = (0)
Taking the equation's partial derivative with regard to y, we obtain:
By taking the equation's partial derivative with respect to y, we arrive at:
-6 sin(y) + 4 sin(x) - 4 cos(x) sin(y) = 0
Evaluating these partial derivatives at the point (47,57/2), we get:
4 cos(47) - 4 cos(57/2) + 1 ≈ -2.8
-6 sin(57/2) + 4 sin(47) - 4 cos(47) sin(57/2) ≈ -4.5
Therefore, the tangent line's slope at the position (47,57/2) of the curve is:
-(-4.5) / (-2.8) ≈ 1.607
Consequently, the tangent line's slope at the point (47,57/2) is roughly 1.607 degrees.
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A walking map of a city has a scale of 1 inch to 2,000 feet. Another map of the same city has a scale of 1 inch to 1,500 feet Which map is smaller? Explain how you know.
Answers
by comparing the two maps, we get that, the map with the scale of 1 inch to 2,000 feet is smaller than the map of scale of 1 inch to 1,500 feet as it includes more area in a single inch.
We are given that:
A map of the city has a scale of 1 inch to 2,000 feet.
This means that 1 inch of the map represents the 2,000 feet of the actual area of the city.
Now, we are given another map which has a scale of 1 inch to 1,500 feet.
This means that 1 inch of the map represents the 1,500 feet of the actual area of the city.
So, by comparing the two maps, we get that, the map with the scale of 1 inch to 2,000 feet is smaller as it includes more area in a single inch.
Therefore. by comparing the two maps, we get that, the map with the scale of 1 inch to 2,000 feet is smaller than the map of scale of 1 inch to 1,500 feet as it includes more area in a single inch.
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The temperature inside the freezer is −10°C and the temperature of the room is 32°C. How much higher is the temperature of the room than the temperature inside the freezer?
Answers
Answer:
42°C
Step-by-step explanation:
32-(-10) =
32 + 10 = 42
Minus a negative makes a positive
A nurse provides a back massage as a palliative care measure to a client who is unconscious, grimacing, and restless. Which of the following findings should the nurse identify as indicating a therapeutic response? (Select all that apply.)
A. the shoulders droop
B. the facial muscles relax
C. the RR increases
D. the pulse is within the expected range
E. the client draws his legs into a fetal position
Answers
A nurse provides a back massage as a palliative care measure to a client who is unconscious, grimacing, and restless.
The therapeutic response that the nurse should identify in the client after a back massage includes relaxing of facial muscles and the pulse remaining within the expected range.
Massage is a fundamental nursing measure that is often utilized as part of palliative care for patients. The purpose of back massage is to promote relaxation, improve blood circulation, reduce muscle tension, and alleviate pain, stress, and anxiety. The nursing assessment of the patient before and after the massage is essential to determine its effectiveness as a therapeutic intervention for the patient.
When providing back massage as a palliative care measure to an unconscious, grimacing, and restless client, the nurse should identify several therapeutic responses as follows;
The shoulders droop: The nurse should expect the shoulders of the client to relax during massage therapy. If this occurs, it is a sign that the patient is experiencing relaxation and tension relief.
The facial muscles relax: Relaxation of the facial muscles is a common therapeutic response during back massage. The nurse should observe the patient's face for any signs of relaxation, which may include softening of facial lines, eyelids drooping, or a general expression of peacefulness.
The respiratory rate (RR) decreases: The nurse should expect the client's respiratory rate to decrease during a back massage. This is because relaxation stimulates the parasympathetic nervous system, resulting in decreased respiratory rate, heart rate, and blood pressure.
The pulse is within the expected range: The nurse should expect the client's pulse to remain within the expected range during a back massage. A normal pulse rate is between 60-100 beats per minute for adults. If the pulse remains within this range, it is a sign that the patient is responding positively to the massage therapy.
In conclusion, providing back massage as a palliative care measure to an unconscious, grimacing, and restless client can help to promote relaxation, improve blood circulation, reduce muscle tension, and alleviate pain, stress, and anxiety. The nurse should identify therapeutic responses in the patient during the massage therapy, which may include relaxation of the shoulders, facial muscles, decreased respiratory rate, and pulse remaining within the expected range.
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Lucy is going to walk in a fundraising event to raise money for her school band. Her mother has agreed to donate $7.50 to the school for each mile that Lucy walks, plus an additional $25.
What equation represents y, the total amount of money Lucy's mother will donate if Lucy walks x miles during the event?
Answers
Answer: y = $7.50x + $25
Step-by-step explanation:
From the question, we are informed that Lucy is going to walk in a fundraising event to raise money for her school band and her mother has agreed to donate $7.50 to the school for each mile that Lucy walks, plus an additional $25.
The equation that represents y, the total amount of money Lucy's mother will donate if Lucy walks x miles during the event will be:
= ($.750 × x) + $25
y = $7.50x + $25
Since Lucy walks x Mike's, we multiply x by $7.50 and then add the answer to the additional $25 which is the answer gotten above.
How many solutions does the equation 6z + 1 = 2(3z - 1) have?
Answers
Answer:
none
Step-by-step explanation:
You want the number of solutions to the equation ...
6z + 1 = 2(3z - 1)
Simplify6z +1 = 6z -2
3 = 0 . . . . . . . . . . add 2 -6z to both sides
There are no values of z that will make this false statement true.
There are no solutions to the equation.
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Colleen has a prepaid phone card with $40 on it. It costs her $0.25 for each minute she spends on the phone. How much money will be left on the card if she speaks for 60 minutes?
Answers
Answer:she will have $25 left .
Step-by-step explanation:
0.25(60) = 15
$40 - $15 = $ 25
NEED QUICKThe sum of x and 3 is the same as the 5 less than 3x. Find x
Answers
Let's begin by identifying key information given to us:
\(\begin{gathered} x+3=3x-5 \\ \text{Put like terms together, we have:} \\ \text{Subtract ''x'' from both sides, we have:} \\ x-x+3=3x-x-5 \\ 3=2x-5 \\ Add\text{ ''5'' to both sides, we have:} \\ 3+5=2x-5+5 \\ 8=2x\Rightarrow2x=8 \\ 2x=8 \\ \frac{2}{2}x=\frac{8}{2} \\ x=4 \end{gathered}\)Aubree bought snacks for her team's practice. She bought a bag of oranges for $3.48 and a 6-pack of juice bottles. The total cost before tax was $9.78. How much was each bottle of juice?
Answers
Answer:
the answer is 1.05$
Step-by-step explanation:
Solve for x and simplify 2x<15
Answers
Answer:
x < 7.5
Step-by-step explanation:
What is $60 increased by 15%
Answers
60, percentage increased by 15% (percent) of its value = 69
PLease help me thank you if you do have a good day
Answers
Answer:
acceleration
Step-by-step explanation:
use POE:
the object is moving because the graph is not a straight line
the object is not slowing down because the graph is going up
there is not a constant speed because the line is exponential not linear
the only one left is a. acceleration
8x3 + 125 which expression represents the correct factorization of the polynomial?.
Answers
The expression that represents the correct factorization of the polynomial 8x³ + 125 exists (2x + 5) (4x² - 10x + 25)
What is meant by polynomial expression?Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable).
A polynomial is not an expression that contains a variable with exponents that are negative or fractional, divides by a variable, or has a variable inside a radical.
Let the given polynomial expression be 8x³ + 125
The expression 8x³ + 125 can be rewritten as (2x)³ + 5³
By using the sum of cubes formula, we get
(2x)³ + 5³ = (2x + 5)( ((2x)² - 2x(5) + 5²)
8x³ + 125 = (2x + 5) (4x² - 10x + 25)
Therefore, the expression that represents the correct factorization of the polynomial 8x³ + 125 is (2x + 5) (4x² - 10x + 25)
The complete question is:
A polynomial expression of degree three is shown below. 8x^3 + 125 Which expression represents the correct factorization of the polynomial?
A (2x + 5)(4x + 10x + 25)
B (2x + 5)(4x + 10x-25)
C (2x + 5)(4x - 10x +25)
D (4x + 25)(2x - 10x+5)
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Jerome solved a system of equations and found that it had an infinite number of solutions. Which system could be the system that Jerome solved
Answers
One example of a system of equations that has infinite solutions is given by:
x + y = 2.
2x + 2y = 4.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
A system will have infinite solutions when the two equations are multiples, hence one example is given by:
x + y = 2.
2x + 2y = 4.
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Prove that the union of three subspaces of V is a subspace iff one of the subspaces contains the other two.
I can do this problem when I am working in only two subspaces of V
but I don't know how to do it with three.
What I tried is: If one of the subspaces contains the other two, Then their union is obviously a subspace because the subspace that contains them is a subspace. (Is this sufficient??).
If the union of three subspaces is a subspace..... How do I prove that one of the subspaces must contain the other two from here?
*When proving this for two I said that there is an element in one of the subspaces that is not the other and proved by contradiction that one of the subspaces must be contained in the other. How would I do this for three?
Answers
If the union of three subspaces of V is a subspace, then one of the subspaces must contain the other two. In other words, if V is a vector space and U, W, and X are subspaces of V, then U ∪ W ∪ X is a subspace of V if and only if one of U, W, and X contains the other two.
Let's suppose that V is a vector space and U, W, and X are subspaces of V such that U ∪ W ∪ X is a subspace of V. This implies that U ∪ W ∪ X contains the zero vector since it is a subspace of V.
Then, the proof will take three parts:Part 1: WLOG, assume that U contains the zero vector. This means that W and X are subspaces of U ∪ W ∪ X.
Part 2: Show that either W is a subset of X or X is a subset of W.Part 3: Since U is a subspace of U ∪ W ∪ X, it follows that W is a subset of U or X is a subset of U. Without loss of generality, assume that W is a subset of U. Then, X is also a subset of U because U ∪ W ∪ X is a subspace of V.
Hence, the proof is complete.
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how would you solve this?
Answers
Answer:
angle one is 40 degrees
Step-by-step explanation:
I'm pretty sure that the measurements of the line should be 180 and 180-140 = 40.
Evaluate the expression 5k2 - 7k when k = 3
Answers
Answer:
24
Step-by-step explanation:
In this question, you have to solve by plugging in the value to the "k" variable and solve.
Solve:
5(3)^2 - 7(3)
3^2 = 9
5(9) - 7(3)
45 - 7(3)
45 - 21 = 24
Your final answer would be 24.
Answer:
24
Step-by-step explanation:
5(3)^2 - 7(3)
5(9) - 21
45 - 21
24
) suppose that the group of ten students consists of six freshmen and four sophomores. in how many different ways can four equal scholarships be distributed if at least two of the scholarships should be awarded to freshmen?
Answers
There are 90 different ways in which the four scholarships can be distributed such that at least two are awarded to freshman students.
We first need to determine the number of ways in which we can choose two of the six freshman students to receive scholarships. This can be done using the binomial coefficient formula: \(${6 \choose 2} = 15$\).
Next, we need to determine the number of ways in which we can choose two of the four sophomore students to receive scholarships. This can also be done using the binomial coefficient formula: \(${4 \choose 2} = 6$\)
Finally, we need to multiply these two values together to get the total number of ways in which the scholarships can be distributed: 15 * 6 = 90. Therefore, there are 90 different ways in which the four scholarships can be distributed such that at least two are awarded to freshman students.
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Find the value of x.
Answers
Answer:
x=67º
Step-by-step explanation:
First since the supplementary angle next to 157º is in the triangle, we can find that. 180-157 = 23. Then we can use triangle angle sum theorem to find x. 180-(23+90) = 67º
$5 box of cereal: 40% discount
Answers
Fill in the blank to make the ratios equivalent.
20: 160
1:
Answers
Answer:
8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
1/x=20/160
20x=160
x=8