Total cards left
52-12=40Total hearts left
13-3=10Probability
P(Heart)=10/40=1/4Option B
Answer:
[tex]\sf F. \quad \dfrac{1}{4}[/tex]
Step-by-step explanation:
A deck of 52 playing cards contains 13 hearts.
If Sara has 12 cards from this deck in her hand and 3 of them are hearts, then:
Total cards remaining in the deck
= total deck - cards Sara has
= 52 - 12
= 40
Total hearts left in the remaining deck
= total heart cards - heart cards Sara has
= 13 - 3
= 10
So there are 40 cards in the deck and 10 of them are hearts.
Probability Formula[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Therefore, the probability that a card drawn at random from the remainder of the deck will be a heart is:
[tex]\begin{aligned}\implies \sf P(heart) & =\dfrac{\textsf{number of hearts in remaining deck}}{\textsf{total cards in remaining deck}}\\\\ & =\dfrac{10}{40}\\ \\& =\dfrac{1}{4}\end{aligned}[/tex]
I need help with answer (3/4) 1/8=
Answer:
3/32Step-by-step explanation:
3/4 * 1/8 = 3*1 / 4*8
3 / 32 is the solution.
boys and girls are in a group. student is chosen at random probability of choosing a girls is 5/10 what's the least number of girls that can be chosen in the group.
Answer:
Step-by-step explanation:
Find the sum.
(y+5) + (3y-9)
The sum is given by - f(y) = 4(y -1).
We have the following expression -
(y + 5) + (3y - 9)
We have to evaluate the above sum.
Add the following expressions - f(x) = 3x + 10 and g(x) = 6 - x.Now -
f(x) + g(x) = 3x + 9 - (6 - x)
f(x) + g(x) = 3x + 10 - 6 + x
f(x) + g(x) = 4x + 4
f(x) + g(x) = 4(x + 1)
According to the question, we have -
(y + 5) + (3y - 9)
Assume that the sum is represented by the function f(y).
Solving, we get -
f(y) = y + 5 + 3y - 9
f(y) = y + 3y + 5 - 9
f(y) = 4y - 4
f(y) = 4(y - 1)
Hence, the sum is given by - f(y) = 4(y -1).
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Which side in the smallest triangle would correspond with HI in the largest triangle?
A.) IK
B.) IJ
C.) None of the sides correspond with HI
D.) JK
The side of the small triangle that will correspond to the side of HI is side IK.
How to find corresponding side of similar triangles?Similar triangles are triangles that have the same shape but different size.
In similar triangles, corresponding sides are always in the same ratio.
The corresponding angles are equal.
Therefore, the side of the small triangle that will correspond to the side of HI is side IK.
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Select the correct answer.
Simplify the polynomial expression.
3x(-2x + 7) - 5(x - 1)(4x - 3)
OA. -26x2 + 56x - 15
B.
14x214x + 15
OC. -26x2 + 21x - 15
OD. -2x2 + 14x - 2
To simplify a polynomial expression, we can expand parentheses by multiplying the terms within with the coefficient outside of them and add like terms.
Solving the Question[tex]3x(-2x + 7) - 5(x - 1)(4x - 3)[/tex]
⇒ Open up the parentheses
[tex]=(3x*(-2x) + 3x*7) - 5(x(4x - 3)-1(4x-3))\\=(-6x^2 + 21x) - 5(4x^2 - 3x-4x+3)\\=-6x^2 + 21x - 5(4x^2 - 7x+3)=-6x^2 + 21x - (20x^2 - 35x+15)\\=-6x^2 + 21x - 20x^2 + 35x-15\\=- 26x^2 + 56x-15[/tex]
Answer[tex]- 26x^2 + 56x-15[/tex]
For tax purposes, a car rental company assumes each car in their fleet depreciates by 7% per year. If the initial value of a car is $32,200.00, what will the value be when the car is 9 years old?
6. A 20-foot vertical pole casts a 12-foot
shadow shown below. Will wants to find the
length of the shadow cast by the 14-foot
pole.
20 pole
14 pole
12 shadow
x shadow
Answer:
6
Step-by-step explanation:
I believe so because the 20 pole took away six so im guessing the 41 pole will to the same
The length of the shadow cast by the 14-foot pole is 8.4 shadows.
We have,
From the figure given,
The two triangles are similar since the corresponding sides and angles are given equal.
This means,
The ratio of the corresponding sides is equal.
So,
20/14 = 12/x _______(1)
Where x is the length of the shadow cast by the 14-foot pole.
Now,
Solving for x from (1).
20/14 = 12/x
Divide 12 on both sides.
20 / (14 x 12) = 1/x
20/168 = 1/x
Cross multiply.
x = 168/20
x = 8.4 shadow.
Thus,
The length of the shadow cast by the 14-foot pole is 8.4 shadows.
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In the expression 3x2 + y − 5, which of the following terms does not have a variable?
a cylindrical tank has a radius of 15 feet and a height of 45 feet of water can tank hold
Answer:
Your answer is 31808.6 but if your rounding the answer will be 31809
Step-by-step explanation:
The eqaution would be " v = 3.14 x r^2 x h"
The scatter plot shows the number of perishable and nonperishable items customers purchased at a market.
Question 1
How many people bought 5 nonperishable items?
Enter your answer in the box.
Question 2
What is the median number of perishable items purchased?
Enter your answer in the box.
Question 3
How many people bought the same number of perishable and nonperishable items?
Enter your answer in the box.
Based on the scatter plot on perishable and nonperishable items purchased by customers, the following is true:
Purchased 5 nonperishable items - 3 people.Median number of perishable items = 7 perishable items. People bought same number of perishable and nonperishable = 2 people. What does the scatterplot show?Looking at the y-axis which shows the number of nonperishable items bought, the number of dots we find at 5 is 3 which means 3 people bought 5 nonperishable items.
The median of perishable items requires that we order the perishable items bought:
2, 2, 5, 6, 7, 8, 9, 10, 11
The median is 7 perishable items.
The number of people with the same number of perishable and nonperishables are 2 people.
One purchased 8 nonperishables and 8 perishables and the other purchased 9 of both items.
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Help! How would I solve this trig identity?
Using simpler trigonometric identities, the given identity was proven below.
How to solve the trigonometric identity?
Remember that:
[tex]sec(x) = \frac{1}{cos(x)} \\\\tan(x) = \frac{sin(x)}{cos(x)}[/tex]
Then the identity can be rewritten as:
[tex]sec^4(x) - sen^2(x) = tan^4(x) + tan^2(x)\\\\\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)} = \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)} \\\\[/tex]
Now we can multiply both sides by cos⁴(x) to get:
[tex]\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)} = \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)} \\\\\\\\cos^4(x)*(\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)}) = cos^4(x)*( \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)})\\\\1 - cos^2(x) = sin^4(x) + cos^2(x)*sin^2(x)\\\\1 - cos^2(x) = sin^2(x)*sin^2(x) + cos^2(x)*sin^2(x)[/tex]
Now we can use the identity:
sin²(x) + cos²(x) = 1
[tex]1 - cos^2(x) = sin^2(x)*(sin^2(x) + cos^2(x)) = sin^2(x)\\\\1 = sin^2(x) + cos^2(x) = 1[/tex]
Thus, the identity was proven.
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Based on the circle graph how many pounds of milk and eggs does the average American consume each year PLS EXPLAIN FOR BRAINLEST
Answer:
Milk and Eggs = 552
Step-by-step explanation:
First add all of the other percentages together. (70%), 100%-70%=30%. 30% of 1840 = 552.
Answer:
H. 552
Step-by-step explanation:
Circle graph information:
Milk and eggs = x%Fruits and vegetables = 38%Cereals = 10%Meat and fish = 10%Sugar = 8%Fats and oils = 4%Total consumption = 1840 pounds per person
First, calculate the percentage of milk and eggs (the value of x).
Total percentages = 100%
⇒ x + 38 + 10 + 10 + 8 + 4 = 100
⇒ x + 70 = 100
⇒ x = 30
Therefore, 30% of food consumption is milk and eggs.
To calculate the number of pounds of milk and eggs the average American consumes each year, simply find 30% of the total consumption:
= 30% of 1840
= 30% × 1840
[tex]=\sf \dfrac{30}{100} \times 1840[/tex]
= 552
Therefore, the average American consumes 552 pounds of milk and eggs each year.
What is the measure of arc bec in circle d
The measure of arc BEC in circle D is 134°
Circle GeometryFrom the question, we are to determine the measure of arc BEC
Measure of arc BEC = 2 × m∠BAC
First, we will determine the measure of angle ACB
From one of the circle theorems,
The angle subtended by an arc of a circle is twice the angle it subtends anywhere on the circle's circumference
∴ m∠ACB = 1/2 × 76°
m∠ACB = 38°
Then,
m∠BAC + m∠ACB + m∠ABC = 180° (Sum of angles in a triangle)
m∠BAC + 38° + 75° = 180°
m∠BAC + 113° = 180°
m∠BAC = 180°- 113°
m∠BAC = 67°
Then,
Measure of arc BEC = 2 × m∠BAC
Measure of arc BEC = 2 × 67°
Measure of arc BEC = 134°
Hence, the measure of arc BEC is 134°
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Concrete blocks are 8in. high. If a 3/8-in. mortar is used, how high will a wall of 12 courses of concrete blocks be?
The altitude of an object with respect to a reference plane or point is termed its height. This includes all parts of the object that add up to its height. Therefore, the height of the wall would be 100.5 inches.
The height of a given object implies the altitude of the object from a reference plane or point.
Therefore given that concrete blocks are 8 inches, then;
total height of mortar required to hold each concrete block = 3/8 inches
Thus, since there are 12 concrete blocks, then 12 sections of mortar would be required to hold 12 blocks starting from the ground.
So that;
total height of mortar required = 3/8 x 12
= 4.5 inches
Total height of all concrete blocks required = 12 x 8
= 96 inches
Therefore, the height of the wall of 12 courses of concrete blocks = 96 + 4.5
= 100.5 inches
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Need help with this word problem!!!!
Answer:
6 seconds after it is launched
Step-by-step explanation:
h(t) = -4t² + 16t + 48
The balloon is at ground level when it lands.
When it is launched, t = 0, and h(0) = 48
When it lands, at time t, h(t) = 0.
-4t² + 16t + 48 = 0
t² - 4t - 12 = 0
(t - 6)(t + 2) = 0
t = 6 or t = -2
The balloon will hit the ground 6 seconds after it is launched.
Gola invests K2,000.00 at 10% simple interest. What is the value of his investment after 2 years?
The value of the investment after 2 years is K2400.00
How to determine the value?The given parameters are:
Principal, P = K2,000.00
Rate, r = 10%
Time, t = 2 years
The value is then calculated as:
Amount = P + PRT
So, we have:
Amount = 2000 + 2000 * 10% * 2
Evaluate
Amount = 2400
Hence, the value of the investment after 2 years is K2400.00
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Given thatx-3+ y and that -2y+3<-1, provide
reasons for each step in the following solution for x.
STATEMENTS
15. x-3+yand -2y+3<-1
16. x>y
17.-24-4
18. y > 2
19. x > 2
15.
16.
17.
18.
19.
Please help
Answer:
h Tu to be a great day of school and
Step-by-step explanation:
great day of school and I have a great day of school and I have a great day of➡ school and I I have a great day of school and I have a great day of school and I have a great yy
1/2 of the people in the clinic are men, 1/3 are elderly, how many people are not elderly or men?
1/6 of the people are not elderly or men
How to determine the proportion?The given parameters are:
Men = 1/2
Elderly = 1/3
The number of people that are not elderly or men are:
People = 1 - Men - Elderly
So, we have:
People = 1 - 1/2 - 1/3
Evaluate
People = 1/6
Hence, 1/6 of the people are not elderly or men
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PLEASE HELP ME! I WILL AWARD BRAINLIEST TO WHOEVER ANSWERS THE QUESTION BEST!
The minimum length Starbucks must build the wheel chair ramp to meet the standards is 23.9ft.
What is a Right angle Triangle?A triangle in which one of the angles is 90 degrees is called a Right angled Triangle.
To find the angle of the ramp, Trigonometric Ratios will be used
As the ramp is forming a right triangle
sin x = 2/22
x = 5.21°
The angle the wheel chair ramp makes with the ground is 5.21°.
If the angle has to be less than 4.8°
Let the length of the wheel chair will be given by y
Then,
2/x < sin4.8
x > 2/sin 4.8
x > 23.9 ft
Therefore the minimum length Starbucks must build the wheel chair ramp to meet the standards is 23.9ft.
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Consider this system of equations. Which shows the second equation written in slope-intercept form?
y=3x-2
10 (x+3/5)= 2y
Answer:
10 (x+3/5)= 2y in slope intercept form
simplify
10x+6=2y
subtract by 2
y=5x+3
Hope This Helps!!!
Marcelina uses a blend of white corn and yellow corn to make tortilla chips at her restaurant. She needs to buy 50kg of corn in total for her next order. White corn costs $0.30 per kilogram, yellow corn costs $0.15 per kilogram, and she wants to spend $12 total.
What does point D represent in this context?
CORRECT (SELECTED)
Marcelina spends less than the intended amount of money and buys the correct amount of corn.
Explanation: Point DDD is below line aaa, so it represents a scenario where she spends less than \$12$12dollar sign, 12. Also, point DDD is on line bbb, so it represents a scenario where she does buy 50\,\text{kg}50kg50, start text, k, g, end text of corn.
In the case above, option b is correct: Marcelina spends the intended amount of money but she bought more than she did intended amount of corn
What is the context about?She buy 50kg of corn in total
White corn costs = $0.30 per kilogram, Yellow corn costs = $0.15 per kilogram,She wants to spend $12 total.So the equation will be:
C= (20, 50) = 20 white, 50 yellow
But 30 while and 20 yellow is needed.
Since C = 20 +50 = 70 corns
While 30 + 20 = 50 corns.
This implies that she spends the intended amount of money but she bought more than she did intended amount of corn and as such, option b is correct.
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You need to Solve 3 math problems
2 coin icons = 2 set numbers
You have to find the number in the last problem
The probability of picking a head and a number 4 is 0.25.
How to calculate the probability?Your information is incomplete and the complete information wasn't found. An overview will be given.
A coin has a head and tail and the probability of choosing either is 1/2 or 0.5.
Let the 2 numbers be 1 and 4. The probability of picking either number will be 1/2 or 0.5 as well.
Here, let the probability of picking a head and a number 4 will be:
= 1/2 × 1/2
= 0.5 × 0.5
= 0.25
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f(x) = 5x + 7
and
g(x) = -2x - 4
Find
g(f(x)) = [?]x + [?]
Answer:
Step-by-step explanation:
f(x)=5x+7
g(x)=-2x-4
g(f(x))=g(5x+7)=-2(5x+7)-4=-10x-14-4=-10x-18
=-10x+(-18)
Which is the equation in slope-intercept form for the line that passes through (−2, 15) and is perpendicular to 2x + 3y = 4?
y=−32x+18
y=32x−12
y=23x+18
y=32x+18
Answer:
y=3/2x + 18
Step-by-step explanation:
So when two lines are perpendicular, that simple means the slope are reciprocals, and the signs are opposite. So for example if one equation had a slope of [tex]\frac{a}{b}[/tex], the equation that is perpendicular, would have a slope of [tex]-\frac{b}{a}[/tex]. So the first step would be to find the slope of 2x+3y=4. To find the slope we can convert it into slope-intercept form which is y=mx+b where m is the slope, and this is done by isolating y, as you can see the y is alone in the slope-intercept form.
Original equation:
2x + 3y = 4
subtract 2x from both equations:
3y = -2x + 4
Divide both sides by 3
y = -2/3x + 4/3
The y-intercept doesn't really matter in this case, what really matters is the slope, and the slope is the coefficient of x, since as x increases by 1, it will increase by the amount of the coefficient, because the slope is rise/run and since the run is 1, if you increase x by 1, the run is the slope, which is the coefficient. The slope in this case is -2/3. So the reciprocal of the slope is 3/2 (notice how the sign is the opposite as well). Now we have the equation
y=3/2x + b
To find the y-intercept, you simply use the point that was given (-2, 15). Plug in -2 as x, and 15 as y to find the value of b
Original equation
y=3/2x + b
Plug in known values:
15 = 3/2(-2) + b
Multiply the fraction:
15 = -6/2 + b
Simplify the fraction:
15 = -3 + b
Add 3 to both sides
18 = b
This gives you the equation
y=3/2x + 18
Simplify: 2(6+1)-|-10|=3x2
Answer:
[tex]\frac{2\sqrt3}{3} = x[/tex]
Step-by-step explanation:
So you want to use PEMDAS to do the equation in order. This means that you'll start by adding 6 and 1 and then multiplying that value by 2
[tex]2(7)-|-10| = 3x^2[/tex]
[tex]14-|-10|=3x^2[/tex]
The absolute value can be defined as the "distance" from 0 which is going to be positive. You can think of it as the positive value of a number so if you have |-b| it will become b, and even if it's already positive, it will remain positive. so the absolute value of -10 is 10 but then it becomes negative again because of the subtraction
[tex]14-10=3x^2[/tex]
[tex]4=3x^2[/tex]
Now you want to solve for x by dividing both sides by 3 and taking the square root of both sides to isolate x
[tex]\frac{4}{3} = x^2[/tex]
[tex]\sqrt{\frac{4}{3}}=x[/tex]
You can distribute the square root across division since [tex](\frac{a}{b})^c = \frac{a^c}{b^c}[/tex] and the square root can be defined as [tex]x^{0.5}[/tex] since [tex]a^b * a^c = a^{b+c}[/tex] because if you spread it out it's really just [tex](a * a * a ... b\ amount \ of \ times) * (a * a * a ... c\ amount\ of\ times)[/tex] which can be simplified to (a * a * a... (b + c) amount of times) if that makes any sense. Anyways using this property you'll get [tex]a^{0.50} * a^{0.50} = a^{0.50 + 0.50} = a^1 = a[/tex]. If you look at it you'll notice a^0.50 multiplied by it self gives you a... sounds like the square root, which it is. So now the equation becomes
[tex]\frac{\sqrt{4}}{\sqrt{3}}=x[/tex]
[tex]\frac{2}{\sqrt3}[/tex]
Now if you look at the equation you'll notice there's a radical in the denominator, which can be rationalized by multiplying by sqrt(3)\sqrt(3) which is 1 except it makes the denominator 3 and keeps the original value
[tex]\frac{2}{\sqrt3} * \frac{\sqrt3}{\sqrt3}=x\\\frac{2\sqrt{3}}{3} = x[/tex]
A light year, the distance light travels in 1 year, is approximately 5.9×10^12 miles. A nearby galaxy is approximately 5.1×10^6 light years from our galaxy. Find the distance in miles between our galaxy and the nearby galaxy.
The distance in miles between our galaxy and the nearby galaxy is 5.99 * 10^12 miles
Difference between exponentsGiven the following parameters
Distance that light travels = 5.9×10^12 miles
Distance in near galaxy = 5.1×10^6miles
Find the difference
Distance = 5.9×10^12 - 5.1×10^6
Distance = 5.99 * 10^12 miles
Hence the distance in miles between our galaxy and the nearby galaxy is 5.99 * 10^12 miles
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A dance team fundraiser there is a pie toss going on and Claudia is tossing pies at her coach… The path of the pie models a Quadratic , And the height is shown in this table what is the maximum height of the pie question
The maximum height of the pie based on the information given is 124.
How to depict the height?From the information given in the table, it can be seen that the time and the height of the pie was given in the table.
In this case, the maximum height of the pie based on the information given is 124. This can be seen at 4 seconds.
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What is the volume of this hemisphere
Answer: 294.34 m^3
Step-by-step explanation: The formula for the volume of a hemisphere is 2/3 * 3.14 * radius cubed (r^3). Plugging in the values, we have 2/3 * 3.14 * 5.2^3, and we get roughly 294.339 m^3, or rounded to the nearest hundredth, 294.34 m^3.
Hope this helped!
Identify the type of function graphed to the right. linear exponential other as x increases by 1 unit, what is the exponential growth factor?
The type of function is Exponential.
What is a Linear function?The function whose graph is in the linear straight line then that function is considered a linear function.
An example of this is 2x+3
What is an Exponential function?An exponential function is a model or a relationship in which there is a constant change in the independent variable that gives the same change in proportionality.
The given function is not showing a linear growth which means there is no straight line so the function will be exponential.
When x increases by 1 unit then the growth factor will be 3/1 = 3
So the exponential growth factor is 3.
What is the exponential growth factor?Exponential growth is like a pattern of data that shows a huge increase with passing time, and by creating the curve for an exponential function.
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The domain for f(x) and g(x) is the set of all real numbers.
Let f(x) = 2x- + x - 3 and g(x) = x - 1.
Find f(x) • g(x).
The product of f(x) and g(x) is 3x²-6x+3
What is a Function?A function is a law that relates a dependent and independent variable with each other.
The domain of f(x) and g(x) is all real numbers
f(x) = 2x + x - 3 and g(x) = x - 1.
Then f(x).g(x) = (2x + x - 3) * ( x - 1)
f(x).g(x) = 2x² -2x +x²-x-3x+3
f(x).g(x) =3x²-6x+3
Therefore, the product of f(x) and g(x) is 3x²-6x+3.
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