Given:
Two cards are drawn from a standard deck of cards without replacement.
To find:
The probability of drawing a heart and a club in that order.
Solution:
We have,
Total number of cards = 52
Number of cards of each suit (Spade, club, diamond, heart) = 13
The probability of drawing a heart card is:
[tex]P(Heart)=\dfrac{\text{Number of heart cards}}{\text{Total number of cards}}[/tex]
[tex]P(Heart)=\dfrac{13}{52}[/tex]
[tex]P(Heart)=\dfrac{1}{4}[/tex]
Now, the number of remaining card is 51. So, the probability of drawing a club card is:
[tex]P(club)=\dfrac{\text{Number of club cards}}{\text{Total number of remaining cards}}[/tex]
[tex]P(club)=\dfrac{13}{51}[/tex]
Using these probabilities, the probability of drawing a heart and a club in that order is:
[tex]P(\text{Heart and club})=P(\text{Heart})\times P(\text{Club})[/tex]
[tex]P(\text{Heart and club})=\dfrac{1}{4}\times \dfrac{13}{51}[/tex]
[tex]P(\text{Heart and club})=\dfrac{13}{204}[/tex]
Therefore, the required probability is [tex]\dfrac{13}{204}[/tex].
sum of -7g and 4g+2
The sum of the given two expressions -7g and 4g+2 is -3g+2.
What are algrbraic expressions?The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown number using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.
What are the types of algebraic expressions?There are mainly 3 types of algebraic expressions which are:
Monomial ExpressionBinomial ExpressionPolynomial ExpressionThe sum of given expressions , -7g and 4g+2 can be performed as follows:
-7g + (4g + 2)
= (-7+4)g + 2
= -3g + 2
To learn more about algebraic sum visit:
https://brainly.com/question/19245500
#SPJ1
Hi Mhanifa, can u answer my last post/question? This is my last question btw. Thank you for all. You helped me a lot.❤️
find the area of each shaded region
Answer:
#712*16 - 1/2*12*14 = 108 cm²#81/2*10*4 - 1/2*5*3 = 12.5 cm²#93.14(4² - 2²) = 37.68 in²#1010² - 3.14*10²/4 = 21.5 cm²#116² - 3.14*6²/4 = 7.74 m²#123.14(4²/2 - 2²) = 12.56 cm²#131/2(12 + 20)*12 - 12² = 48 cm²#143.14(14² - 7²) = 461.58 cm²Draw a diagram of x + 2 and a separate diagram of 3x when x is 2.
The graph of the equation x + 2 would be a straight line that starts at the point (-2, 0) and goes up 2 units on the y-axis. So, the line would pass through the point (0,2) and would be parallel to the x-axis.
The graph of the equation 3x when x is 2 would be a straight line that starts at the point (0,0) and goes up 6 units on the y-axis for each 1 unit on the x-axis. So, the line would pass through the point (2,6) and would have a slope of 3.
What is diagram in mathematics?In mathematics, a diagram is a visual representation of mathematical concepts or ideas. Diagrams can take many forms, such as graphs, charts, illustrations, and figures, and can be used to help explain or understand mathematical concepts.
For example, a graph is a type of diagram that is used to represent the relationship between two variables. It is commonly used in algebra and calculus to show the relationship between an independent variable (x-axis) and a dependent variable (y-axis).
A chart is a type of diagram that is used to organize and present data. It is commonly used in statistics to show the distribution of data or to compare different sets of data.
Learn more about diagram in brainly.com/question/11729094
#SPJ1
Which graph best represents the solution to the following pair of equations?
y = −x − 5
y = 2x + 4
Answer:
Two lines having equations y is equal to negative x minus 5 and y is equal to 2 times x plus 4 are plotted. These 2 lines intersect at the ordered pair negative 3, negative 2.
Step-by-step explanation:
Obviously, the appropriate graph will be one with the two lines plotted. Properly plotted, they will intersect at (-3, -2).
Hakims car travels 600 feet in 20 seconds. Andres mortar cycle travels 300 feet in 12 seconds. Which is faster, the car or the motorcycle?
Find the unit rates
Compare the unit rates
-help please-
Answer:
Hakims car travels 600 feet in 20 seconds. Andres mortar cycle travels 300 feet in 12 seconds. Which is faster, the car or the motorcycle?
The car is faster
Find the unit rates
The car is going 30 feet in 1 second(600 divide by 20 = 30)
The motorcycle is gonig 25 feet in 1 second(300 divide by 12 = 25)
Compare the unit rates
30 > 25
Step-by-step explanation:
Answer:
Hakim's car is faster.
Step-by-step explanation:
Hakim's car takes 20 seconds to go 600 feet. Andre's motorcycle takes 24 seconds to go 600 feet.
So for Hakim, the unit rate are 30 feet per second because 600/20 = 30
For Andre, the unit rate is 25 feet per second because 600/24 = 25
Hakim's car goes faster because 30 is greater than 25.
14% of a certain food is fat. Out of 400 total grams, how many grams are not fat?
Answer:
344 grams are not fat
Step-by-step explanation:
400 x (100% - 14%) =
400 x 86% = 344
Hope that helps! :)
-Aphrodite
Bookerville has a record of 12 inches of rain in 5 days. How much will it have to rain on Friday to beat the record by one tenth of an inch
The amount of rain required would be 2.5 inches.
What is the addition?
Addition is a mathematical operation that represents the process of combining two or more numbers together. The result of this operation is called the sum. The addition operation is often represented using the symbol "+", and it can be used to add any two or more numbers together.
To beat the record by one-tenth of an inch, an additional 0.1 inches of rain must fall.
Currently, the average amount of rain per day is 12 inches / 5 days = 2.4 inches per day.
So, the amount of rain that must fall on Friday to beat the record by one-tenth of an inch is 2.4 inches + 0.1 inches = 2.5 inches
Hence, the amount of rain required would be 2.5 inches.
To learn more about the addition, visit:
https://brainly.com/question/24536701
#SPJ1
16. WHAT is a parallelogram.
W
T
1070
y
36°
42°
H
А
X
y =
Step-by-step explanation:
hope this helps you out with the problem
12 pounds of corn cost Marcus $15.60. How much would five pounds of corn
cost at the same unit rate?
Answer:
$6.30
Step-by-step explanation:
Alright, so, to find the unit rate (how much 1 pound of corn would cost) you would divide $15.60 by 12 which would get you $1.30.
Cost of 1 pound of corn = $1.30
So the unit rate = $1.30
Now that you know the unit rate, or how much 1 pound would cost, you can find out how much 5 pounds would cost:
$1.30 x 5 = $6.50
Steps:
1. $15.60/12 = $1.30
2. $1.30 x 5 = $6.50
Five pounds of corn costs $6.50 at a unit rate of $1.30.
Hope this helps! :)
if you answer the question Correctly I will give you brainliest.
Answer:
6982 ft squared
Step-by-step explanation:
The area of the trapezoid is 10000 feet square and the area of the square building is 3072 square feet. In order to find the area of the lawn, you need to subtract the area of the building from the area of the trapezoid, which is 6982 feet squared.
Answer:
6982 ft squared
Step-by-step explanation:
Decide if each statement correctly describes a relationship between the categories.
Choose Yes or No for each statement.
Answer:
1.no,2.yes 3.yes 4.no
Step-by-step explanation:
rhombuses are subcategories of squares. some isosceles triangles have angles more than 90 degrees or 90 degrees exact
Consider the following problem:
The length s(t) of the side of the base of a square prism is decreasing at a rate of 7
kilometers per minute and the height h(t) of the prism is increasing at a rate of 10
kilometers per minute. At a certain instant to, the base's side is 4 kilometers and the
height is 9 kilometers. What is the rate of change of the surface area A(t) of the
prism at that instant?
Match each expression with its given value.
The rate of change of surface area is 524.02 square kilometers per minutes.
what is surface area of square prism?The total space occupied by a three-dimensional square prism is called surface area.
What is the rate of change of surface area of the prism?
Given, the decreasing rate of the base side with respect to time, ds/dt = 7 km/min
the increasing rate of height with respect to time, dh/dt = 10 km/min
At a time, t, base side, s = 4 km
and height, h = 9 km
we need to determine the rate of change of surface area with respect to time, d A/dt
from the differentiation chain rule, d A/ dt = d A /dt × ds /ds
d A /dt = d A/ ds × ds /dt ... equation 1
we know that the surface area for prism, A = 2s² + 4sh
if we differentiate with respect to s then we find d A /ds
d/ds (A) = d/ ds (2s² + 4sh)
d A /ds = 4s + 4h +4s dh/ds ...... equation 2
now dh /ds = dh /ds × dt /dt [ using differentiation chain rule]
dh/ds = dh/ dt× dt/ds
d h/ ds = dh/dt × 1/ ds/dt
it stated earlier that dh/ dt = 10 and ds /dt = 7
dh / ds = 10/7
putting this value in equation 2, we get
d A /ds = 4s +4h + 4s ×10/7
as we know at time t, s= 4 and h = 9
d A /ds = 4 × 4 + 4 ×9 +4×4 ×10 /7
d A /ds = 74.86
putting the value d A /ds in equation 1, we get
d A /dt = d A /ds × ds/ dt
d A/ dt = 74.86 × 7
d A /dt = 524.02 km² / min
hence, the rate of change of surface area = 524.02 square kilometers per minutes
To learn more about chain rule for differentiation visit:
https://brainly.com/question/28484294
#SPJ1
the following sample data are from a normal population : 10,8,12,,15,13,11,6,5
The population of a city decreases by 0.9% per year. If this year's population is pp, which expression does NOT represent next year's population?
0.9910.991
0.991p0.991p
(1-0.009)p(1−0.009)p
1p-0.009p1p−0.009p
The expression does not represent next year's population is 0.991. The correct option is A.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the population of a city decreases by 0.9% per year. The expression for the population depreciation is,
Population = ( 100% - 0.9%)P
Population = (1 - 0.009)P
Population = 0.991P
Hence, the expression not representing the depreciation is 0.991.
To know more about an expression follow
https://brainly.com/question/29183615
#SPJ1
Does the table below represent a proportional relationship? DUE PLSS
A. Yes, because all the ratios of y to x are equal to 2.
B. Yes, because all the ratios of y to x are equal to 3.
C. No, because all the ratios of y to x are not equal.
D. No, because all the numbers are positive.
Answer: The answer to your question is the letter B. May want to assess it before answering.
What is the circumference of the circle that has a radius of 8.6mm
Answer:
C= 54.O4
.................
The radius of a cylinder is 3 cm and the height is 6 cm.
Find the Surface Area. (hint: Use the answer from the previous question.)
4811
5411
0 3617
9211
Answer:
B. 54π
Step-by-step explanation:
Surface area of cylinder = 2πrh + 2πr²
Radius = 3 cm
Height = 6 cm
Plug in the values
Surface area of the cylinder = 2*π*3*6 + 2*π*3²
Surface area = 36π + 18π
Surface area = 54π
The 5th grade is going on a trip. There are 285 students in the grade. Buses hold 30 passengers. How many buses are needed for the entire fifth grade to go on their trip?
Answer:
10 busses
Step-by-step explanation:
285÷30=9.5
9.5 would round up to 10
If
f
(
x
)
=
2
x
4
−
3
x
+
3
f(x)=2x
4
−3x+3, then what is the remainder when
f
(
x
)
f(x) is divided by
x
−
1
x−1?
Answer:
If
f
(
x
)
=
2
x
4
−
3
x
+
3
f(x)=2x
4
−3x+3, then what is the remainder when
f
(
Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 38 randomly selected people who train in groups, and finds that they run a mean of 49.5 miles per week. Assume that the population standard deviation for group runners is known to be 1.1 miles per week. She also interviews a random sample of 33 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 2.6 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2.
Required:
Draw a conclusion and interpret the decision.
Answer:
conclude that there is no significant evidence to support the claim that difference exists between the mean number of miles run by the two groups.
Step-by-step explanation:
H0 : μ1 = μ2
H0 : μ1 ≠ μ2
The test statistic :
(x1 - x2) / √(s1²/n1) + (s2²/n2)
(49.5 - 48.5) / √(1.1²/38) + (2.6²/33)
1 / √0.2366905
Test statistic = 2.055
Using the Pvalue from Tstatistic calculator :
df = (smaller sample - 1) = 33 - 1 = 32
Pvalue from Test score calculator = 0.048
Pvalue > α ; Fail to reject the null ;
Hence, conclude that there is no significant evidence to support the claim that difference exists between the mean number of miles run by the two groups.
How many times will Anna need to fill the measuring cup to measure 78 7 8 cup of turnips? If Anna divides the ingredients equally into 4 pots, how many cups of onions will she need in each pot?
Answer:
Step-by-step explanation:
3 너 도넛
Consider the function f (x) = x.What effect does subtracting 2 from the input have on the graph of the function?
The effect of subtracting 2 from the input on the graph of the function is a translation of 2 units to the right.
What effect does subtracting 2 from the input?For any function f(x), we define a horizontal translation of N units as:
g(x) = f(x + N)
And what this does, is translate the graph N units horizontally.
if N > 0, then the translation is to the left.
if N < 0, then the translation is to the right.
Here we want to subtract 2 from the input, so we will get:
f(x - 2)
By using the definition above, we know that we will have a translation of 2 units to the right.
Learn more about translations by reading:
https://brainly.com/question/24850937
#SPJ1
Find the slope of the line that has an equation of 4x-2y=6
4x - 2y = 6
2y = 4x - 6
y = (4x - 6)/2
y = 2x - 3
The population of the city of Woodville is growing at a constant rate. The expression 38,000 + 2,400x models Woodville's population.
Which THREE statements are correct?
es )
A)
x represents the number of years
B)
2,400 represents the current population.
C)
38,000 represents the current population.
D)
2,400 represents the population growth yearly.
E)
38,000 represents the population growth yearly
Bananas FOR $1.00 Oranges - 6 FOR $1.50 Peaches - 4 for $1.28 Frankie mother tells Him that they need 5 Bananas 15 Oranges. And 10 peaches For the Salad. Determine the total cost of the amount of fruit that " FRAnkie needs.
Answer:
Mizuki is here to help! The answer will be $11.95
Step-by-step explanation:
Ok so... Frankie wants 5 bananas, 15 oranges, and 10 peaches for the salad right?
First, let's find the price of the 5 bananas. We multiply 1 by 5 and get 5, so $5 is the cost for the bananas he is going to spend.
Next, let's find the price for 15 oranges. First, we will divide 15 by 6, which will end up with 2.5. Then, we multiply 1.5 by 2.5 which will be 3.75. The price for the oranges he is going to buy is $3.75.
Then, let's find the price of the 10 peaches. The step is similar from the way we solved the price of oranges. We divide 10 by 4 and get 2.5. Next, we will multiply 1.28 by 2.5 and get 3.2. The price for peaches is $3.2.
Finally, let's add up 5, 3.75, and 3.2! The total should be 11.95! That will be your answer!
Given the equation below, if x = 4, what is the value of y? y=14x
Answer:
the answer would be 56.
y=14(4)
y=56
In ΔRST, sin T = 1/5, m∠R = 30, and r = 15. What is the length of t?
Answer:
t = 6Step-by-step explanation:
Given ΔRST with:
sin ∠T = 1/5m ∠R = 30°r = 15t = ?Solution
We know t is opposite ∠T and r is opposite ∠R.
Use the law of sines to find the missing value of t.
r / sin ∠R = t / sin ∠TSubstitute the known values and solve for t:
15 / sin (30°) = t / (1/5)15 / (1/2) = 5t30 = 5tt = 30/5t = 6Answer:
t = 6
Step-by-step explanation:
In ΔRST:
Angle R is opposite side r.Angle S is opposite side s.Angle T is opposite side t.Sine Rule
[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Given:
sin T = ¹/₅R = 30°r = 15Substitute the given values into the Sine Rule formula and solve for t:
[tex]\implies \sf \dfrac{r}{\sin R}=\dfrac{s}{\sin S}=\dfrac{t}{\sin T}[/tex]
[tex]\implies \sf \dfrac{15}{\sin 30^{\circ}}=\dfrac{t}{\frac{1}{5}}[/tex]
[tex]\implies \sf \dfrac{15}{\sin 30^{\circ}}=5t[/tex]
[tex]\implies \sf t=\dfrac{15}{5 \sin 30^{\circ}}[/tex]
[tex]\implies \sf t=\dfrac{15}{5 \cdot \frac{1}{2}}[/tex]
[tex]\implies \sf t=\dfrac{15}{\frac{5}{2}}[/tex]
[tex]\implies \sf t=15 \cdot \dfrac{2}{5}[/tex]
[tex]\implies \sf t=\dfrac{30}{5}[/tex]
[tex]\implies \sf t=6[/tex]
Learn more about the Sine Rule here:
https://brainly.com/question/27089170
https://brainly.com/question/28033514
-3/5(1+5n) =102
Solve for n
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
David is saving $250 to buy a bicycle. He saved $8 each week for 12 weeks. He wants to buy the bicycle in 7 more weeks. How much does David need to save each week?
Answer:
He would need to save $22 dollars each week to pay for the bike in 7 weeks.
Step-by-step explanation:
We can figure out how many he has saved up already by multiplying the number of weeks (12) by how much he saved each week ($8) which equals $96. Now we have to subtract $96 from $250 which equals $154. Now we need divide this amount by the remaining weeks until he wants to purchase his bike (7), so 154/7 which equals $22.
So he needs to pay 22 dollars each week to pay off the bike in seven weeks
Find the mean, median, and mode for 0, 4, 6, 11, 9, 8, 9, 1, 5, 9, 7. Round to the nearest tenth if needed.
Answer:
Mean - 6.2 Median - 7 Mode - 9
Step-by-step explanation:
You can find the mean by adding all the given numbers and dividing them by how many numbers you added.
The median is the middle value of the set of numbers, order them from least to greatest and find the middle value.
Mode is the number that occurs the most.