The probability of getting at least one Canadian quarter is 0.6
How to determine the probability of getting at least one Canadian quarter?
This is a binomial probability experiment. We are going to use the binomial distribution formula for determining the probability of x successes:
P(x = r) = nCr . p^r . q^n-r
Where n = number of trials, p = probability of success and q = probability of failure, x = number of Canadian quarters
39 U.S. quarters + 11 Canadian quarters coins = 50 coins
Given: n = 4 (four quarters picked), p = 11/50 = 0.22, q = 1-p =1-0.22 = 0.78
Probability at least one Canadian quarter = 1 - Probability of no Canadian quarter
P(x≥1) = 1 - P(x = 0)
= 1 - (4C0×0.22⁰× 0.78⁴⁻⁰ )
= 1 - 0.4
= 0.6
Therefore, the probability of getting at least one Canadian quarter is 0.6
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Which graph represents the function f(x) = 4/x
Answer:
Step-by-step explanation:
HELP!!! I am having trouble understanding how to do these problems. Can someone please help explain how to complete these problems. Thank you so much!
1. Find the measure of <6.
2. Find the measure of <4.
Answer:
1=180 2=90
Step-by-step explanation:
1=∠1 and ∠2 are supplementary, so m∠2 = 180° - x°. ∠2 and ∠6 are corresponding angles. So, m∠6 = 180° - x°.
2=Their measures are equal, so m∠4 = 90 . When two lines intersect to form one right angle, they form four right angles.
Answer:
∠4 = 55°
∠6 = 35°
Step-by-step explanation:
Finding the unknown angles:In ΔABC,
35 + 90 + ∠4 = 180° {Sum of all angles of triangle}
125 +∠4 = 180
∠4 = 180 - 125
∠4 = 55°
Linear pair: If in two adjacent angles, the non-common arms form a straight line, then the two angles are called linear pair and they add up to 180.
∠7 + ∠8 = 180° {linear pair}
90 + ∠7 = 180°
∠7 = 180 - 90
∠7 = 90°
In ΔACD,
∠6 + ∠4+ ∠7 = 180 {Sum of all angles of triangle}
∠6 + 55 + 90 = 180
∠6 + 145 = 180
∠6 = 180 - 145
∠6 = 35°
1. Fourteen cars were randomly chosen at a used car lot. The age of each car and its sale price are shown in
the following table.
Answer: $10,252.87
Step-by-step explanation:
Based on the linear model of data, the price of the car that is 10 year old is approximately 10,000.
Linear model.
Basically, the linear model describes the relationship between a dependent variable, y, and one or more independent variables, X. Where the dependent variable is also called the response variable. And the independent variables are also called explanatory or predictor variables.
Given,
Here we have the table of data that contains the fourteen cars were randomly chosen at a used car lot and the age of each car and its sale price.
Now, we have to find the sale price for the 10 year old car.
In order to find the price of the 10 year old car, we have to plot these given table on the graph.
Then we get the graph like the following.
By looking at the graph, the sales price of the 10 year old car is predicted as approximately 10,000,
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The following angles are supplementary to each other.
mzA= (4x + 30) and mzB = (2x - 30)°
Determine x.
15
20
30
60
Answer:
30
Step-by-step explanation:
Supplementary angles add to 180°.
[tex]4x+30+2x-30=180 \\ \\ 6x=180 \\ \\ x=30[/tex]
Salespeople at a certain company have a quota to meet each month. On average, they hit the quota 68% of the
time. If a salesperson hits the quota, the probability of being promoted in the next six months is 0.41. If a person
doesn't hit the quota, the probability of being promoted is 0.14.
Use the tree diagram to complete each statement.
The probability of no promotion, given that a salesperson hit the quota: A is
The probability of a promotion, given that a salesperson missed the quota: B is
The probability of no promotion, given that a salesperson missed the quota: C is
The probability that a salesperson hit the quota and got promoted: D is
V
Done
The probability that a salesperson hit the quota, given that the salesperson was promoted, using the tree diagram,: is option c 0.86
What is a probability?
The probability of an event in an experiment is calculated by the division of the number of desired outcomes by the number of total outcomes in the experiment.
From the tree diagram, there are two ways to obtain the promotion:
0.41 of 0.68 (hit the quota).
0.14 of 0.32 (did not hit the quota).
Hence the probability of getting a promotion is:
P(A) = 0.41 x 0.68 + 0.14 x 0.32 = 0.3236.
The probability of both getting a promotion and hitting the quota is:
P(A and B) = 0.41 x 0.68 = 0.2788.
Hence the conditional probability is:
P(B|A) = P(A and B)/P(A) = 0.2788/0.3236 = 0.86. (approximately).
The probability that a salesperson hit the quota, given that the salesperson was promoted, using the tree diagram,: is option c 0.86
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Naomi is going to invest $78,000 and leave it in an account for 7 years. Assuming the
interest is compounded daily, what interest rate, to the nearest hundredth of a
percent, would be required in order for Naomi to end up with $91,000?
In order to get the total amount $91,000 at the end of the 7 year, the interest rate is 2.2% on compound interest basis.
Compound Interest:
The general form to calculate the compound interest is written as,
A = P(1 + r/n)ⁿˣ
where
A = Accrued amount (principal + interest)
P = Principal amount
r = Annual nominal interest rate as a decimal
n = number of compounding periods per unit of time
x = time in decimal years
Given,
Naomi is going to invest $78,000 and leave it in an account for 7 years. Assuming the interest is compounded daily.
Here we need to find the nearest hundredth of a percent, would be required in order for Naomi to end up with $91,000.
Here we have to solve for rate r as a decimal
[tex]r = n[(A/P)^{1/nt} - 1][/tex]
r = 365 × [(91,000.00/78,000.00)1/(365)(7) - 1]
r = 0.022022202
Then convert r to R as a percentage
R = r * 100
R = 0.022022202 * 100
R = 2.202%/year
Therefore, the interest rate required to get a total amount of $91,000.00 from compound interest on a principal of $78,000.00 compounded 365 times per year over 7 years is 2.202% per year.
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Question
A farmer notices that there is a linear relationship between the number of bean stalks, n, she plants and the yield, Y. When
she plants 3 stalks, each plant yields 115 ounces of beans. When she plants 8 stalks, each plant yields 190 ounces of beans.
Write the linear equation, Y(n), that correctly represents this situation.
Provide your answer below:
Y(n)=
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The equation that represent the given situation is y = 15x + 70
When she plants 3 stalks, each plant yields 115 ounces of beans
The first point = (3, 115)
When she plants 8 stalks, each plant yields 190 ounces of beans
The second point = (8, 190)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line m = (190-115) / (8-3)
= 75/5
= 15
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
Choose one point and substitute the values in the equation
y - 115 = 15(x - 3)
y - 115 = 15x - 45
y = 15x - 45 + 115
y = 15x + 70
Hence, the equation that represent the given situation is y = 15x + 70
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BRO PLEASE THIS IS SO HARD
Joanna was eager to know her score on the science final exam. Ms. Filer would release the scores once she graded all exams. Ms. Filer had less than 15 exams left to grade.
Which number line represents the number of exams Ms. Filer had left to grade?
number line with a closed circle on number 15 and line shaded left
number line with an open circle on number 15 and line shaded leftt
number line with an open circle on number 15 and line shaded right
number line with a closed circle on number 15 and line shaded right
Question 2(Multiple Choice Worth 5 points)
(Solving One-Step Equations with Rational Numbers LC)
Given the equation five eighths plus h equals eleven over eight, determine the value of h.
six eighths
sixteen over eighteen
fifty five over sixty four
eight over six
Question 3(Multiple Choice Worth 5 points)
(Translating Algebraic Inequalities MC)
Water boils at a minimum temperature of 100 degrees Celsius. Which inequality represents this scenario?
100 > b
100 < b
100 ≤ b
100 ≥ b
Question 4(Multiple Choice Worth 5 points)
(Writing One-Step Equations with IntegersMC)
Mario set a goal to run 150 miles this month to prepare for a marathon. So far this month, he has run 75 miles. Write and solve an equation to show how many miles Mario has left to run this month to reach his goal.
m − 75 = 150; m = 225 miles
m + 75 = 150; m = 75 miles
75m = 150; m = 2 miles
m over 75 equals 150; m = 11,250 miles
Question 5(Multiple Choice Worth 5 points)
(Solving One-Step Equations with Integers LC)
Given the equation f + 24 = −3, solve for f.
−72
−27
−21
8
Question 6(Multiple Choice Worth 5 points)
(Writing One-Step Equations with IntegersMC)
Max organized a community toy drive for the holidays. He asked each family to donate a total of 4 gifts. Twelve families participated in the toy drive. Write and solve an equation that represents how many gifts were donated.
4g = 12; g = 3 gifts
g + 4 = 12; g = 8 gifts
g − 4 = 12; g = 16 gifts
g divided by 12 equals 4; g = 48 gifts
Question 7(Multiple Choice Worth 5 points)
(Solving One-Step Equations with Integers LC)
Given the equation 17 equals y over -3, solve for y.
−51
−14
20
51
Question 8(Multiple Choice Worth 5 points)
(Writing One-Step Equations with IntegersMC)
Bella is baking 42 cookies for the holiday party tonight. She baked 29 before leaving for school and will bake the rest when she returns home.
Which equation shows how many cookies Bella will bake when she returns home?
42 = x + 29
42 = x − 29
42 = 29x
29 = x − 42
Question 9(Multiple Choice Worth 5 points)
(Evaluating Inequalities MC)
Determine which integer makes the inequality 6(n − 5) < 3(n + 4) true.
S:{11}
S:{14}
S:{30}
S:{42}
Question 10(Multiple Choice Worth 5 points)
(Solving One-Step Equations with Rational Numbers LC)
Given the equation 5.24w = 16.506, solve for w.
86.49
21.746
11.266
3.15
Question 11(Multiple Choice Worth 5 points)
(Writing One-Step Equations with IntegersMC)
Pete was building a doghouse for his dog, Chip. He made the door 36 inches tall. The height of the door was twice the height of the window in the doghouse.
Write an equation to determine the height of the window.
36 = 2h
36 = 2 + h
36 = h − 2
36 equals h over 2
Question 12(Multiple Choice Worth 5 points)
(Evaluating Equations MC)
Determine which integer in the solution set will make the equation true.
8x − 4 = 2(2x + 4)
S: {−4, 0, 3, 12}
−4
12
0
3
The number line which represents the number of exams Ms. Filer had left to grade is "number line with an open circle on number 15 and line shaded left". option B
The value of h from the equation "five eighths plus h equals eleven over eight" is "six eighths". option AThe inequality which represent "Water boils at a minimum temperature of 100 degrees Celsius is 100 ≥ b. option DThe equation which shows how many miles Mario has left to run this month to reach his goal is m + 75 = 150; m = 75 miles. option BThe value of f from the equation f + 24 = -3 is -27. option BThe equation that represents how many gifts were donated is g divided by 12 equals 4; g = 48 gifts. option DThe value of y from the equation 17 equals y over -3 is - 51. option A.The equation which shows how many cookies Bella will bake when she returns home is 42 = x + 29. option AThe integer which makes the inequality 6(n − 5) < 3(n + 4) true is S:{14}. option BHow to solve equation?five eighths plus h equals eleven over eight, determine the value of h.
5/8 + h = 11/8
substract 5/8 from both sides
h = 11/8 - 5/8
h = 6/8
h = 3/4
Water boils at a minimum temperature of 100 degrees Celsius.
The inequality:
100 ≥ b
Mario total goal for the month = Number of miles Mario has left to run this month to reach her goal + number of miles Mario has run so far
150 = m + 75
substract 75 from both sides
150 - 75 = m
75 = m
The equation f + 24 = −3, solve for f.
f + 24 = -3
substract 24 from both sides
f = -3 - 24
f = -27
Number of gifts each family donates = 4
Number of families = 12
Total gifts donated = g
The equation:
g / 12 = 4
cross product
g = 12 × 4
g = 48
The equation 17 equals y over -3, solve for y.
17 = y / -3
cross product
17 × -3 = y
-51 = y
Number of cookies Bella is baking = 42
Number of cookies she has baked = 29
Number of cookies left for Bella to bake = x
The equation:
42 = x + 29
substract 29 from both sides
42 - 29 = x
13 = x
The inequality:
6(n − 5) < 3(n + 4)
open parenthesis
6n - 30 = 3n + 12
6n - 3n = 12 + 30
3n = 42
divide both sides by 3
n = 42/3
n = 14
The equation 5.24w = 16.506, solve for w.
5.24w = 16.506
divide both sides by 5.24
w = 16.506 / 5.24
w = 3.15
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How to convert lot into units
Answer: divide the area value by 1e+6
Step-by-step explanation:
2x < 15
answer and how to solve please
Answer:
×= -7½
Step-by-step explanation:
2x<15
2x<15=0
2x= -15
x= -15/2
x= -7½
HELP PLEASE! 66pts!
Solve for x. SHOW WORK!
2^(3x+1)=1/4
The solution of the exponential equation is x = -1
How to find the value of x?
We want to solve the exponential equation:
2^(3x + 1) = 1/4
If we apply the natural logarithm in both sides of that equation, we will get:
ln( 2^(3x + 1) ) = ln( 1/4)
(3x + 1)*ln(2) = ln(1/4)
3x*ln(2) = ln(1/4) - ln(2)
x = (ln(1/4) - ln(2))/(3*ln(2)) = -1
The value of x is -1
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Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or
simplified fractions.
-4x-5y+6z = 5
-3x+6y-2z = 4
5x+9y-3z = 1
The solution of the system using Cramer's Rule is x= -0.53, y=0.78 and z=1.13.
In the given question we have to solve the system using the Cramer's rule.
The given equations are
-4x-5y+6z = 5
-3x+6y-2z = 4
5x+9y-3z = 1
From the Cramer's rule
[tex]\left[\begin{array}{ccc}-4&-5&6\\-3&6&-2\\5&9&-3\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}5\\4\\1\end{array}\right][/tex]
Here,
A = [tex]\left[\begin{array}{ccc}-4&-5&6\\-3&6&-2\\5&9&-3\end{array}\right][/tex]
X= [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]
B = [tex]\left[\begin{array}{ccc}5\\4\\1\end{array}\right][/tex]
Now D=|A|
D= [tex]\left|\begin{array}{ccc}-4&-5&6\\-3&6&-2\\5&9&-3\end{array}\right|[/tex]
D= [tex]-4\left|\begin{array}{ccc}6&-2\\9&-3\end{array}\right|-(-5)\left|\begin{array}{ccc}-3&-2\\5&-3\end{array}\right|+6\left|\begin{array}{ccc}-3&6\\5&9\end{array}\right|[/tex]
D= -4[6×(-3)-(-2)×9]+5[(-3)×(-3)-(-2)×5]+6[(-3)×9-5×6]
D= -4[-18+18]+5[9+10]+6[-27-30]
D= -4×0+5×19+6×(-57)
D= 0+95-342
D= -247
[tex]D_{x}=\left[\begin{array}{ccc}5&-5&6\\4&6&-2\\1&9&-3\end{array}\right][/tex]
Simplifying the matrix
[tex]D_{x}=5\left|\begin{array}{ccc}6&-2\\9&-3\end{array}\right|-(-5)\left|\begin{array}{ccc}4&-2\\1&-3\end{array}\right|+6\left|\begin{array}{ccc}4&6\\1&9\end{array}\right|[/tex]
[tex]D_{x}[/tex] = 5[6×(-3)-(-2)×9]+5[4×(-3)-(-2)×1]+6[4×9-1×6]
[tex]D_{x}[/tex] = 5[-18+18]+5[-12+2]+6[36-6]
[tex]D_{x}[/tex] = 5×0+5×(-10)+6×30
[tex]D_{x}[/tex] = 0-50+180
[tex]D_{x}[/tex] = 130
[tex]D_{y}=\left[\begin{array}{ccc}-4&5&6\\-3&4&-2\\5&1&-3\end{array}\right][/tex]
Simplifying the matrix
[tex]D_{y}= -4\left|\begin{array}{ccc}4&-2\\1&-3\end{array}\right|-5\left|\begin{array}{ccc}-3&-2\\5&-3\end{array}\right|+6\left|\begin{array}{ccc}-3&4\\5&1\end{array}\right|[/tex]
[tex]D_{y}[/tex] = -4[4×(-3)-(-2)×1]-5[(-3)×(-3)-(-2)×5]+6[(-3)×1-4×5]
[tex]D_{y}[/tex] = -4[-12+2]-5[9+10]+6[-3-20]
[tex]D_{y}[/tex] = (-4)×(-10)-5×19+6×(-23)
[tex]D_{y}[/tex] = 40-95-138
[tex]D_{y}[/tex] = -193
[tex]D_{z}=\left[\begin{array}{ccc}-4&-5&5\\-3&6&4\\5&9&1\end{array}\right][/tex]
Simplifying the matrix
[tex]D_{z}=-4\left|\begin{array}{ccc}6&4\\9&1\end{array}\right|-(-5)\left|\begin{array}{ccc}-3&4\\5&1\end{array}\right|+5\left|\begin{array}{ccc}-3&6\\5&9\end{array}\right|[/tex]
[tex]D_{z}[/tex] = -4[6×1-4×9]+5[1×(-3)-4×5]+5[(-3)×9-5×6]
[tex]D_{z}[/tex] = -4[6-36]+5[-3-20]+5[-27-30]
[tex]D_{z}[/tex] = (-4)×(-30)+5×(-23)+5×(-57)
[tex]D_{z}[/tex] = 120-115-285
[tex]D_{z}[/tex] = -280
As we know that; x=Dx/D, y=Dy/D, z=Dz/D
x=130/(-247)
x= -0.53
y=(-193)/(-247)
y=0.78
z=(-280)/(-247)
z=1.13
Hence, the solution of the system using Cramer's Rule is x= -0.53, y=0.78 and z=1.13.
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What expression represents the verbal phrase?
one-half times a number m plus twenty-five
The expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.
According to the question,
We have the following information,
The given verbal phrase is one-half times a number m plus twenty-five.
Now, we will solve it step by step.
Now, we will first find one-half times a number m. We know that we will replace the word times with multiplication. So, we have the following expression:
m/2
Now, adding 25 to this term, we have the following final expression:
m/2+25
Hence, the expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.
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You invest $6000 in a restaurant. The investment has a return of 12%. How
much do you receive for your investment after 30 months?
The return received after 30 months on an investment of $6000 will be $1800.
According to the question,
We have the following information:
You invest $6000 in a restaurant. The investment has a return of 12% per year.
We know that the following formula is used to find the simple interest on the amount:
Simple interest = principal*rate*time/100
Now, we have the following values in this case which we will put in the formula:
Principal = $6000
Rate = 12%
Time = 2.5 years
Simple interest = (6000*12*2.5)/100
Simple interest = $1800
Hence, the amount received after 30 months on an investment of $6000 will be $1800.
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PLEASE ANSWER!!!! WILL GIVE BRAIN THINGY
Answer:
No solutions
Step-by-step explanation:
-5y+7/2y=-5-3/2y-4
+3/2y. +3/2y
-5y+3/2y+7/2y=-5-4
-5y+10/2y=-9
-5y+5y=-9
0=-9
No solutions
Hopes this helps please mark brainliest
3) Karen, her brother Dan, Dana, and her sister Randi own a pizza restaurant, Karen and Dan each own 2/7 of the
restaurant. The remaining share is owned equally by Dana and Randi. Exactly what fraction of the business
does Dana own?
Dana owns [tex]\frac{3}{14}[/tex] fraction of the business
How to calculate the fractions?
*Identify a fraction: When writing fractions, one number is placed above the dividing line and one number is written underneath it.
*Find the numerator: The numerator—the number at the top—indicates the number of elements that make up the fraction.
*find the denominator: The denominator is the figure at the bottom. This number reveals how many components there are in the total number.
Let us take the fraction shared by Dana and Randi as x
So the equation becomes
[tex]\frac{2}{7} +\frac{2}{7} +x+x=1[/tex]
⇒ [tex]\frac{4}{7}+2x=1[/tex]
⇒2x=1-[tex]\frac{4}{7}[/tex]
⇒[tex]2x=\frac{7-4}{7}[/tex]
⇒[tex]2x=\frac{3}{7}[/tex]
⇒[tex]x=\frac{3}{7*2}[/tex]
⇒[tex]x=\frac{3}{14}[/tex]
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find the area between the curve y=x^2-3x for x between 1 and 8
The area between the curve y = x^2 - 3x for x between 1 and 8 is 1343 / 3 square units.
First, let us understand the area under the curve:
A definite integral between two points is used to calculate the area under a curve between them. Integrate y = f(x) between the limits of a and b to determine the area under the curve y = f(x) between x = a and x = b. This area can be estimated by integrating with specified limitations.
We are given:
y = x^2 - 3x
We need to find the area between the curve y = x^2 - 3x for x between 1 and 8.
Now,
Integrate the given function:
Integration y = Integration x^2 - Integration 3x
y = [x^(2 + 1) / (2 + 1)] ^ 8 _1 - [3x^(1 + 1) / (1 + 1)] ^ 8 _1
y = [x^3 / 3] ^ 8 _1 - [3x^2 / 2] ^ 8 _1
y = [8^3 / 3 - 1^3 / 3] - [3 * 8^2 / 2 - 1 * 8^2 / 2]
y = [512 / 3 - 1 / 3] - [96 - 32]
y = 1535 / 3 - 64
y = 1535 - 192 / 3
y = 1343 / 3 square units.
So, the area is 1343 / 3 square units.
Thus, the area between the curve y = x^2 - 3x for x between 1 and 8 is 1343 / 3 square units.
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On December 13,2007 one U.S. dollar was worth 0.69 euro
On that date, how many dollars was 110.66 euro worth?
Round your answer to the nearest hundredth of a dollar.
-----need a response back ASAP!----------
On that date, how many euro was 77.65 dollars worth?
Round your answer to the nearest hundredth of a euro.
On that date, 110.66 euro was worth 160.38 dollars.
On that date, 77.65 dollars was worth 53.58 euro.
How to calculate the value?Given that one U.S. dollar was worth 0.69 euro, the dollar that was 110.66 euro worth will be:
= Amount of euro / Rate
= 110.66 / 0.69
= 160.38 dollars
The euro that 77.65 dollars was worth will be:
= 77.65 × 0.69
= 53.58 euro
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Hunter is going to see a movie and is taking his 4 kids. Each movie ticket
costs $12 and there are an assortment of snacks available to purchase for $5
each. How much total money would Hunter have to pay for his family if he
were to buy 4 snacks for everybody to share? How much would Hunter have
to pay if he bought a snacks for everybody to share?
Answer:
$80
Step-by-step explanation:
hunter+ kid 1+kid 2+kid 3+kid 4= 60 dollars just for tickets
4 snacks= 20 dollars for snacks
$60+$20=$80
PLEASE MARK BRAINIEST
Emma recorded the weight of her kitten in ounces on certain days for 24 days. The data are shown in the scatterplot.
Answer:
can you show me it so i can help
Step-by-step explanation:
Trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on the graph. What are the coordinates of pre-image point H?
The coordinates of pre-image point H is (c) (3, 2)
How to determine the coordinates of pre-image point H?The graph represents the given parameter
On the graph, we have the coordinate of point H' (i.e. the image) to be
H' = (-3, -2)
The transformation rule is given as
Rotation 180° about the origin
Mathematically, this is represented as
(x, y) = (-x, -y)
This implies that:
H = (3, 2)
So, the coordinates are (3, 2)
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Use the following model to answer the question.
Which division problem is shown by the model?
OA. 0.66÷3= 0.22
O B. 0.663 = 0.26
OC. 0.78÷3= 0.62
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D. 0.78÷3= 0.26
D
G
Option D is correct answer, The given model in the picture shows the division problem as: 0.78 ÷ 3 = 0.26.
What is division?
Along with addition, multiplication, and subtraction, division is one of the four basic mathematical operations. The act of separating anything into smaller groups so that each one has the same amount of items is known as division. It is a mathematical operation that is used to distribute and group things equally.
we can count that, there are 26 cubic blocks in each square in the picture,
10 each are vertically in two rows and 6 are horizontally present.
And there are total of 3 such squares present each with 26 cubic blocks.
So these all totals to 78 cubic blocks which is divided in 3 squares and in each squares there are 26 cubic blocks.
Therefore, the division problem representing this can be written as:
0.78 ÷ 3 = 0.26
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Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: −3, ordered pair: (−5,3)
Answer:
[tex] \huge{ \boxed{y = - 3x - 12}}[/tex]
Step-by-step explanation:
Equation of a line in slope-intercept form is given by
[tex]y = mx + c[/tex]
where
m is the slope
c is the y intercept
From the question
m = -3
In order to find c we substitute the point (−5,3) into the equation y = mx + c
We have
[tex]3 = - 3( - 5) + c \\ 3 = 15 + c \\ c =3 - 15 \\ c = - 12 [/tex]
We now substitute c and m into the main equation
We have the final answer as
[tex]y = - 3x - 12[/tex]
Hope this helps you
Lim x->1 sinx - sin1/x-1
The limit Lim x→1 (sinx - sin1)/(x - 1) = cos1
What is the limit of a function?The limit of a function f(x) as x tends to a is the value of the function f(x) as x tends to a. It is written as [tex]\lim_{x \to a} f(x) = L[/tex]
How to find the given limit of the function?GIven that we require the limit given as [tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1}[/tex]
So, substituting the value of x = 1 into the given equation, we have that
[tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = \frac{sin1 - sin1}{1 - 1} \\= \frac{0}{0}[/tex]
Since 0/0 is one of the inderterminate forms, we use the L'hopital's rule to find the limit of the given function.
What is L'hopital's rule?L'hopital's rule states that if [tex]\lim_{x \to a} f(x) = \lim_{x \to a} g(x) = 0[/tex] and f'(x) and g'(x) exist then [tex]\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}[/tex]
Let the variables be
f(x) = sinx - sin1 and g(x) = x - 1So, since we know that
[tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = \frac{0}{0}[/tex],
So, [tex]\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}[/tex]
So, we differentiate both the numerator and denominator and find the limit.
So,
[tex]\lim_{x \to 1} \frac{f'(x)}{g'(x)} = \lim_{x \to 1} \frac{\frac{d(sinx - sin1)}{dx} }{\frac{d(x - 1)}{dx} } \\= \lim_{x \to 1} \frac{cosx - 0}{1 - 0} \\= \lim_{x \to 1}cosx \\= cos1[/tex]
So, [tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = cos1[/tex]
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Tricia made a 72% on her science test. if she got 18 problem correct, how many questions were on the test?
Answer: 25 questions
Step-by-step explanation:
ACTIVITY 7
In a pack of cards, there are 52 cards. There are 4 suits diamonds, hearts, spades and
clubs. Each suit has a King, a Queen, a Jack and an Ace. It also has cards for 2. 3. 4.
5, 6, 7, 8, 9 and 10 If the pack has been shuffled so that the cards are in no particular
order, and you select one card from the pack without looking, what is the probability of
selecting
a) a Queen
b) a red Queen
c) a Jack of Hearts
d) a Jack of Hearts or Diamonds
e) any club
f) a six or a seven
g) a black six
h) a picture card (Jack, Queen or King)
Answer:
Step-by-step explanation:
abcdefgh
write the mixed number 4 2/5 as an improper fraction
Answer:
[tex]\frac{22}{5}[/tex]
Step-by-step explanation:
To write a mixed number as an improper fraction, you start by converting the "number part" into a fraction.
For example, in this problem 4 is the number part, and we want to rewrite 4 as fraction with a denominator of 5. To do this, we multiply four by 5, which is twenty and put this over 5: [tex]\frac{20}{5}[/tex]. This would be a fraction representing 4(you can check through division).
Next, we need to add [tex]\frac{2}{5}[/tex] to this. [tex]\frac{2}{5} +\frac{20}{5}[/tex] would just be [tex]\frac{22}{5}[/tex] because 20 + 2 = 22.
The following inequalities form a system.
y is greater than or equal to two-thirds times x plus 2
y is less than negative one-third times x plus 1
Which ordered pair is included in the solution to this system?
(−6, −3)
(−6, −2)
(−6, 3)
(−6, 4)
From the graph, the ordered pair that is included in the solution to the given system is (-6, -2). The correct option is the second option (−6, −2)
Solving system of linear inequalities using graphFrom the question, we are to determine the ordered pair that is included in the solution to the given system of inequalities
The given system of inequalities is
y ≥ 2/3(x) + 2
y < -1/3(x) + 1
To determine the ordered pair that is included in the solution, we will graph the given system of linear inequalities.
The graph of the system of linear inequalities is given below.
From the graph, we can observe that (-6, -2) is a solution to the given system of linear inequalities.
Hence, the ordered pair that is a solution is (-6, -2)
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Answer:
Option B: (-6, -2)
Step-by-step explanation:
i took the test xx
calculate the area of this trapezium
Answer:
Step-by-step explanation:
Let the trapezium be B.
Draw a line from the top of the trapezium to it's base and call the triangle formed B.
The base of is 2cm (8cm - 6cm
The area of the triangle = 40cm² ( 5cm x 4cm x 2cm)
Area of the trapezium =. ½ (base x height)
. = 18cm²
Add area of trapezium and triangle.
= 40cm² + 18cm² = 58cm²
.
Consider the function f, where f(x) = 2x2 - x+ 3. Part A Complete the equation to represent f(x + 1). X+Y Select and drag numbers into the empty boxes to correctly complete the equation.
The numeric value of the function f(x) = 2x² - x + 3 at x = x + 1 is given as follows:
f(x + 1) = 2x² + 3x + 4.
How to obtain the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
In this problem, the function is defined as follows:
f(x) = 2x² - x + 3.
The point at which the numeric value is calculated as given by:
x = x + 1.
Hence the numeric value is obtaining replacing the two instances of x in the function by x + 1, as follows:
f(x + 1) = 2(x + 1)² - (x + 1) + 3
f(x + 1) = 2(x² + 2x + 1) - x - 1 + 3
f(x + 1) = 2x² + 4x + 2 - x - 1 + 3
f(x + 1) = 2x² + 3x + 4.
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