The chance of rolling a 5 on a six-sided dice is 1/6, and the probability of getting a tails in a coin toss is 1/2. The total probability of both these independent events occurring is (1/6) * (1/2) = 1/12 or approximately 0.0833 on a decimal scale.
Explanation:The question is asking for the probability of rolling a 5 on a dice and then getting a tails on a coin toss. To get the total probability, we multiply the individual probabilities together.
First, let's consider a fair six-sided die. The chance of rolling a 5 (or any specific number between 1 and 6) is 1/6.
Next, we consider a fair coin, which has two outcomes: heads or tails. So, the probability of getting tails is 1/2.
The total probability of both these events occurring is (1/6) * (1/2) = 1/12. So, the probability of rolling a 5 and then tossing a tail is 1 in 12 or approximately 0.0833 on a decimal scale.
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solve 1.2 = g - (-4.3)
The price of a ticket was increase from 50p to 60p. What is the increase a as a fraction in its simple form? As a percentage of the original price?
Given is the price increase of a ticket from 50p to 60p.
Using the concept of fractions, we can find the ratio of new price to old price as follows :-
[tex] \frac{new \;\; price}{old \;\; price} = \frac{60p}{50p} =\frac{6}{5} [/tex]
So the increase in price is [tex] \frac{6}{5} [/tex] times old price of the ticket.
Using the formula of percentage, we can find the percentage change in price as follows :-
[tex] Percentage = \frac{(new\;\;price \;-\; old\;\;price) }{old \;\; price}*100 \\\\
Percentage = \frac{60p-50p}{50p}*100 \\\\
Percentage = \frac{10p}{50p}*100 \\\\
Percentage = 20\;\% [/tex]
Hence, Percentage increase is 20% of the original price.
I need help for number 13-16 and I also need an explanation please help
In a linear programming graph, the best (optimal) solution always occurs at a point called what?
Answer:
In a linear programming graph, the best optimal solution always occur at a point called:
Extreme Point.
Step-by-step explanation:
As we know that the optimal solution is the solution that is a feasible solution and satisfies the objective function.
The objective solution always exist at the corner point of the feasible region and the objective function is either a minimization or a maximization function and hence such a point will is a objective solution is called a extreme point.
perpendicular to x-6y=7; y-intercept (0,-5). the equation of the line is:
A creek runs along a distance of 16,300 feet. About how many miles long is the creek?
Find the surface area of the composite solid and round to the nearest tenth. Explain your answer.
what is the following product? ^3√24 x ^3√45
The simplified value of the product of [tex]\sqrt[3]{24}\times\sqrt[3]{45}[/tex] is [tex]6\sqrt[3]{5}[/tex].
What are some rules of exponents?Some common rules of exponents are
xᵃ×xᵇ = xᵃ⁺ᵇ.
xᵃ/xᵇ = xᵃ⁻ᵇ.
Addition and subtraction of exponents is only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.
We know when we have the same radical we can simply multiply the values.
Given, [tex]\sqrt[3]{24}\times\sqrt[3]{45}[/tex].
= [tex]\sqrt[3]{24\times45}[/tex].
= [tex]\sqrt[3]{2\times2\times2\times3\times3\times3\times5}[/tex].
= [tex]2\times3\sqrt[3]{5}[/tex].
= [tex]6\sqrt[3]{5}[/tex].
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License plates are made using 2 letters followed by 3 digits. How many plates can be made if repetition of letters and digits is allowed?
What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice 35- x/4 =x/3
ethan took a quiz with 15 questions. if he answered 3/5 of the questions correctly, how many did he get wrong?
A cylinder shaped water tank has a diameter of 10 m and a height of 10 m. What volume of water does the tank hold when it's 75% full?
a yearbook page will show 20 photos displyed in rws each row must contain the same number of photos how many different ways can the photos be arranged
Answer:
6If we need all the rows to be equal, all we are doing is dividing.
20/1= 20
20/2= 10
20/4=5
20/5=4
20/10=2
20/20=1
We have 6 different ways to divide 20!
The price of a condominium is $102,000. The bank requires a 5% down payment and one payment and one point at the time of closing. The cost of the condominium is financed with a 30-year fixed-rate mortage at 8.5%? Find the required down payment.
The required down payment for a condominium priced at $102,000, with a 5% down payment, is $5,100. This is calculated by multiplying the price of the condominium by 0.05. Therefore, the down payment amount is $5,100.
The price of the condominium is $102,000, and the bank requires a 5% down payment. To find the required down payment, we need to calculate 5% of the condominium's price.
Step-by-step solution:
Express 5% as a decimal: 5% = 0.05Multiply the price of the condominium by this decimal: $102,000 * 0.05Perform the multiplication: $102,000 * 0.05 = $5,100Therefore, the required down payment for the condominium is $5,100.
Can you answer these questions for me plz I need them before Monday ty
Gas costs $1.64 a gallon. Elaine spent $23.78 at the gas station.How many gallons of gas did she but?
Answer:
23.78
Step-by-step explanation:
A rectangular prism with a volume of 400 cubic centimeters has the dimensions x + 1 centimeters, 2x centimeters, and x + 6 centimeters. The equation 2x^3 + 14x^2 +12x =400 can be used to find x. What is the length of the longest side? Use a graphing calculator and a system of equations to find the answer.
A) 4 centimeters
B)5 centimeters
C)8 centimeters
D)10 centimeters
The length of the longest side of the rectangular prism is approximately
10 centimeters.
The correct option is D.
What is a prism?In three-dimensional space, a prism is a polyhedron where two ends are similar.
To solve the equation 2x³ + 14x² +12x =400, we first need to rearrange it to the standard form of a cubic equation:
2x³ + 14x² +12x - 400 = 0
We can use a graphing calculator to find the real solutions of this equation, which are approximately x = -8.75, x = 2.16, and x = 5.59.
Since the dimensions of the rectangular prism are x + 1, 2x, and x + 6, we need to find the maximum value of the expression (x + 1)(2x)(x + 6) over the interval [2.16, 5.59]. We can set up a system of inequalities to find this maximum value:
2.16 ≤ x ≤ 5.59
(x + 1)(2x)(x + 6) ≥ 400
Using a graphing calculator, we can graph the function f(x) = (x + 1)(2x)(x + 6) and find the maximum value over the interval [2.16, 5.59]. The maximum value occurs at x ≈ 4.98, and the value of the function at this point is approximately 469.83.
Therefore, the length of the longest side of the rectangular prism is approximately 4.98 + 6 = 10.98 centimeters, which is closest to answer choice D) 10 centimeters.
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120% of a number is 45 find the number
Can you please help me out ?
Use the intercepts to graph the equation 8x - 5y = 40
To graph the equation 8x - 5y = 40, find the x-intercept and y-intercept. The x-intercept is (5,0) and the y-intercept is (0,-8). Plot these points and draw a straight line passing through them.
Explanation:To graph the equation 8x - 5y = 40 using intercepts, we need to find the x-intercept and y-intercept. The x-intercept is the point where the line intersects the x-axis, so let y = 0 and solve for x. The y-intercept is the point where the line intersects the y-axis, so let x = 0 and solve for y.
Setting y = 0, we get 8x - 5(0) = 40, which simplifies to 8x = 40. Solving for x, we find x = 5. So the x-intercept is (5, 0).
Setting x = 0, we get 8(0) - 5y = 40, which simplifies to -5y = 40. Solving for y, we find y = -8. So the y-intercept is (0, -8).
Plotting the x-intercept (5, 0) and the y-intercept (0, -8) on a graph, we can draw a straight line passing through these two points, which is the graph of the equation 8x - 5y = 40.
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If a skateboard is 2 1/2 feet long, what is the length of 4 skateboards in yards?
The length of 4 skateboards is 3 2/3 yards.
What is the length of 4 skateboards in yards?The first step is to convert feet to yards.
1 feet = 1/3 yards
5/2 x 1/3 = 5/6 yards
The second step is to multiply 5/6 yards by 4
5/6 x 4 = 20 / 6 = 3 2/3 yards
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Factor 6y 2 - 48 + 42y
The expression 6y² - 48 + 42y is factored by first rearranging the terms, finding the GCF, and then factoring the resulting trinomial to get 6(y + 8)(y - 1).
To factor the expression 6y² - 48 + 42y, the first step is to rearrange the terms in descending powers of y, which gives us 6y² + 42y - 48. Next, we can look for a greatest common factor (GCF) among the three terms. Observing that each term is divisible by 6, we can factor out 6:
6(y² + 7y - 8)
Now, we need to factor the trinomial within the parentheses. We are looking for two numbers that multiply to give -8 (coefficient of y² times constant term), and add to 7 (coefficient of y term). The numbers +8 and -1 satisfy these conditions:
6(y + 8)(y - 1)
Thus, the original expression 6y² - 48 + 42y factors to 6(y + 8)(y - 1).
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Factor the polynomial: x^2–xy+x–xy^2+y^3–y^2
Mary’s number is eleven more than Jerry’s. The sum of their numbers is 89. What are their numbers?
Mary and Jerry's number will be 39 and 50.The sum of their numbers is 89.Which shows that the obtained answer is correct.
What is a linear equation?It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.
If in the linear equation one variable is present then the equation is known as the linear equation in one variable.
Let, Mary’s number be x
Mary’s number is eleven more than Jerry’s
Jerry's number is x+11
From the given condition sum of their numbers is 89.
[tex]x + (x + 11) = 89\\\\ 2x + 11 = 89\\\\ 2x = 89 - 11\\\\ 2x = 78\\\\ \frac{2x}{2} = \frac{78}{2} \\\\ x = 39[/tex]
Jerry's number will be;
[tex]x+11 \\\\ 39+11 \\\\ 50[/tex]
Hence the Mary and Jerry's number will be 39 and 50.
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A $25,000 purchase decreases 12% in value per year. Determine the values of the purchase after 3 years and after 7 years.
evaluate log (Base3) 9
A rectangular prism has a length of 212 centimeters, a width of 212 centimeters, and a height of 5 centimeters. Justin has a storage container for the prism that has a volume of 35 cubic centimeters. What is the difference between the volume of the prism and the volume of the storage container? Enter your answer in the box as a simplified mixed number or a decimal.
Answer:
[tex]3.75\ cm^{3}[/tex] or [tex]3\frac{3}{4}\ cm^{3}[/tex]
Step-by-step explanation:
step 1
Find the volume of the rectangular prism
we know that
The volume of a rectangular prism is
[tex]V=LWH[/tex]
In this problem we have
[tex]L=2\frac{1}{2}\ cm=\frac{2*2+1}{2}=\frac{5}{2}\ cm[/tex]
[tex]W=2\frac{1}{2}\ cm=\frac{2*2+1}{2}=\frac{5}{2}\ cm[/tex]
[tex]H=5\ cm[/tex]
substitute in the formula
[tex]V=(\frac{5}{2})(\frac{5}{2})(5)=\frac{125}{4}=31.25\ cm^{3}[/tex]
step 2
Find the difference between the volume of the prism and the volume of the storage container
[tex]35\ cm^{3}-31.25\ cm^{3}=3.75\ cm^{3}[/tex]
[tex]3.75=3\frac{3}{4}\ cm^{3}[/tex]
Answer:
3.75
Step-by-step explanation:
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What is the slant height if the surface area is 395.64 square meters? (Use 3.14 for π .) r = 7 of a cone
A. 7
B. 9
C. 11
D. 13
The slant height of a cone with a radius of 7 meters and a surface area of 395.64 square meters is approximately 11 meters, which corresponds to option C.
Explanation:To find the slant height of a cone when you know the radius (r) and the surface area, you can use the formula for the surface area of a cone, which is spelled out as A = πrs + πr², where A is the surface area, r is the radius, and s is the slant height. In this case, you know that the surface area (A) is 395.64 square meters and the radius (r) is 7 meters. So, you can rearrange the formula to solve for the slant height(s) : A - πr² = πrs => (A - πr²)/πr = s.
Insert the values into the formula: s = (395.64 - 3.14*7²) / (3.14*7). By performing these calculations, you'll find that the slant height is approximately equal to 11, which corresponds to option C.
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A Family spends 240.00 per week on food. If this is 16% of their income, what is the families weekly income?
*show work*
The family's weekly income is $1500.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
given that,
A Family spends 240.00 per week on food. If this is 16% of their income.
let,
x = weekly income (in dollars)
16% of x = amount spent on food per week
16% of x = 240
(16/100)*x = 240
0.16*x = 240
0.16*x/0.16 = 240/0.16
x = 1500
Hence, The family's weekly income is $1500.
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A cosmetics company decides to compare its new nail polish product, Bella, with three other nail polish brands: Primrose, Shine, and Glo. In an experiment, participants are divided into four groups. Each group of women is asked to wear nail polish from one of the four brands. The results for Primrose, Shine, and Glo are compared with those for Bella, and a conclusion is drawn. What does the type of nail polish represent in this case?
In this experiment, the type of nail polish represents B. the explanatory variable.
The nail polish brands—Bella, Primrose, Shine, and Glo—are the explanatory variables in the experiment that is being discussed. These are the many conditions or treatments that are being investigated to find out how they affect a certain result.
The primary aim of the experiment is to compare how each type of nail polish performs or is perceived, which requires manipulating the nail polish type and observing the results.
The response variable (or dependent variable) is the outcome that is measured in response to the explanatory variables. This could be factors like durability, appearance, user satisfaction, or any other measurable characteristic related to the nail polish.
Thus, the nail polish brands are the explanatory variables because they are the categories being compared. The response variable would be whatever metric is used to evaluate the performance or characteristics of these nail polishes.
Complete Question:
Select the correct answer. A cosmetics company decides to compare its new nail polish product, Bella, with three other nail polish bra experiment, participants are divided into four groups. Each group of women is asked to wear nail polish from one of the four brands. The results for Primrose, Shine, and Glo are compared with those for Bella, and a conclusion is drawn. What does the type of nail polish represent in this case? A. the control group B. the explanatory variable C. the response group D. the response variable