Answer:
65 miles
Step-by-step explanation:
Given:
k = how many more miles Daniel has to walkGoal = 100 milesDaily miles = 5 milesNumber of days already walked = 7 daysEquation:
5 × 7 + k = 100
Solving:
⇒ 5 × 7 + k = 100
⇒ 35 + k = 100
⇒ k = 100 - 35
⇒ k = 65
A group of pupils take a test. The group consists of 28 boys and 24 girls.
The mean mark for the boys is 28. The mean mark for the girls is 14.
Calculate the mean mark for the whole group.
Give your answer correct to 1 decimal place.
Answer:
21.5 to 1 decimal place.
Step-by-step explanation:
The total number of marks for all the boys = 28*28 = 784 marks.
The total number of marks for all the girls = 24*14 = 336 marks.
So the mean mark for the whole group
= (784+336) / (28+24)
= 1120 / 52
= 21.538
Rick's savings account has a balance of $5000. If he does not make a
withdrawal or deposit, how much money will be in Rick's account if it pays an
annual interest rate of 6% for 8 years compounded quarterly?
Answer:
$8,051.62
Step-by-step explanation:
Compound interest formula
[tex]\sf A=P(1+\frac{r}{n})^{nt}[/tex]
where:
A = final amountP = principalr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = $5000r = 6% = 0.06n = 4t = 8Substituting given values into the formula:
[tex]\implies \sf A=5000(1+\frac{0.06}{4})^{4 \times 8}[/tex]
[tex]\implies \sf A=5000(1.015)^{32}[/tex]
[tex]\implies \sf A=8051.62\:(nearest\:hundredth)[/tex]
Rate of interest
0.06/4=0.015So
Compound ineterest formula to be used
A=P(1+r)^tA=5000(1+0.015)⁴×⁸A=5000(1.015)³²A=$8051.615
67°
X
Find the missing side in the following and round to nearest tenth
Because this is a right triangle, we can use a trigonometric function to solve for the missing side.
Remember: SOH-CAH-TOA
We are given an angle, as well as the adjacent side and hypotenuse. Therefore, we should use the cosine function to solve for x.
cos(67) = x / 15
x = cos(67) * 15
x = 5.9
Answer: 5.9
Hope this helps!
(06.01 LC) A scatter plot is shown. 10 9 8 7 6 5 4 3 2. 0 1 2 3 4 5 6 7 8 9 10 How many outliers does the graph show? (1 point) 01 02 03 4
Answer:
2 outliers
Step-by-step explanation:
(1,9) and (10,7) both are outliers.
There are 2 outliers in the given scatter plot. Therefore, option B is the correct answer.
What does outliers mean in scatter plots?An outlier is a data point that does not fit the rest of the data. It lies outside of a cluster and does not follow the same pattern. Scatter plots can have many outliers, just one outlier, or no outliers.
From the given graph, we can see that coordinates (1, 9) and (10, 7) are not in the cluster.
These two points lies out side the cluster, so these points are outliers.
Therefore, option B is the correct answer.
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Please help me with this math word problem! Please...
Let the price of an adult ticket is x and a child ticket is y .
from the question ,
[tex]6x + 2y = 124 \: \: ...(i) \\ \\ 3x + 5y = 100 \: \: ...(ii)[/tex]
Multiply 2 in eq (ii)
[tex]6x + 10y = 200 \: \: ...(iii)[/tex]
On adding eq (iii) and (i)
[tex]6x + 10y = 200 \\ \\ 6x + 2y = 124[/tex]
we get ,
[tex]8y = 76 \\ \\ y = \frac{76}{8} \\ \\ y = 9.5[/tex]
putting y in eq (i)
[tex]6x + 2y = 124 \\ \\ 6x + 2 \times 9.5 = 124 \\ \\ 6x + 19 = 124 \\ \\ 6x = 124 - 19 \\ \\ 6x = 105 \\ \\ x = \frac{105}{6} \\ \\ x = 17.5[/tex]
The value of x = 17.5 and y = 9.5
Hence , The price of an adult ticket is 17.5 and the price of a child ticket is 9.5 .If f(x) = 2x − x² + 3, find f(x − 4).
Answer:
−x^2+10x−21
Step-by-step explanation:
Hope this helped you! If this is wrong, please tell me and have a good day!
Graph the inequality x < - 10/3
Answer:
Picture Below :)
Step-by-step explanation:
*ta da*
- Have a great day -
negative using self reported delinquency
Answer:
Your question does not make sence
Determine the intervals on which f(x) is x>0 and on which f(x) is x<0.
f(x)=x^5+x^4-3x^3-3x^2-9x-9
Answer:
f(x) > 0 for (-2.203, -1) U (2.203, ∞)f(x) < 0 for (-∞, -2.203) U (-1, 2.203)Step-by-step explanation:
A graph shows real zeros at ±2.203 and -1. The value of f(x) changes sign at each of these.
The positive leading coefficient indicates the graph trends generally upward, so the function will be positive in intervals with an even number of zeros to the right.
f(x) positiveThere are an even number of zeros to the right of x = 2.203 and the interval (-2.203, -1).
f(x) is positive in the intervals (-2.203, -1) or (2.203, ∞).
f(x) negativeThe function will be negative where it is not positive (except at the zeros)
f(x) is negative in the intervals (-∞, -2.203) or (-1, 2.203).
_____
Additional comment
The graph shows the only rational real root of the function is x=-1. Using synthetic division to reduce the polynomial, we find ...
f(x) = (x +1)(x^4 -3x^2 -9)
The remaining factor is a quadratic in x^2, which has roots ...
x = ±√(1.5 ±√11.25)
The real roots are approximately ±2.20320266118. The value 2.203 used above is a stand-in for the exact value √(1.5 +√11.25)).
Find the area K of the triangle.
a=4, b=5, C = 25°
K=
square units
(Round to two decimal places
as
needed.)
Answer:
4.23 square units
Step-by-step explanation:
The area of the triangle is given by the formula ...
K = 1/2ab·sin(C)
__
Filling in the given values, we find the area to be ...
K = 1/2(4)(5)sin(25°) = 4.23 . . . . square units
What number is b?
b +4= 10
Answer:
6
Step-by-step explanation:
b+4=10
-4 .-4
b=6
Answer:
b= 6
Step-by-step explanation:
subtract the answer (10) by the remaining 4, (so 10-4) which equals 6
Compare 4 and -2. Which of the following is true?
Answer:
Your answer is A.
Step-by-step explanation:
Absolute values of any number are positive.
|4| = 2
|-2| = 2
2 = 2 and 4 > -2
C and D can be true, but they are not since less than or greater than doesn't apply if they were less than/greater than or equal, then yes.
Aline has a slope of 6 and includes the points (-9, 0) and (-8, a). What is the value of a?
Submit
Please help
Answer:
a = 6
Step-by-step explanation:
Given information:
Slope = 6
Coordinates: (-9, 0) and (-8, a)
Slope formula = y2 - y1 / x2 - x1
Substitute the given values into the formula.
6 = a - 0 / -8 - (-9)
6 = a - 0 / 1
6 = a - 0
a = 6
hope this helps!! p.s. i really need brainliest :)
1. What is the volume of the cone? (Use 3.14 for *)
904.8 cubic feet
226.2 cubic feet
75.4 cubic feet
301.6 cubic feet
Answer:
C) 75.36 cubic feet
Step-by-step explanation:
Volume of a cone: ⅓hπr²
Given:
r (radius) = 3 fth (height) = 8 ftπ ≈ 3.14Substitute the given values to find the volume:
V = (⅓)(8)(3.14)(3)²
V = (⅓)(8)(3.14)(9)
V = (⅓)(226.08)
V = 75.4 ft³ (nearest tenth)
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-1/2(x+5)=-10 I WONT BREATHE UNTIL U ANSWER ME!!
Step-by-step explanation:
well don't breath just collect like terms and booom
what is the value of x for 3x^2 - x + 9 = 0
Correct option is A)
Consider the given equation,
3
2x
+10.3
x
−9=0
Let ,y=3
x
Now ,
y
2
−10y+9=0
y
2
−9y−y+9=0
y(y−9)−1(y−9)=0
(y−9)(y−1)=0
When,
x−9=0
x=9
Now ,
9=3
x
3
2
=3
x
x=2
When,
y−1=0
y=1
3
x
=1
3
x
=3
0
x=0
x=0,x=2
This is the answer
wich one is a Line of Symmetry with a line going up and down called
a.Horizontal Line of Symmetry
b.Vertical Line of Symmetry
c.Diagonal Line of Symmetry
Your answer is B.
Vertical goes straight up and down.
Horizontal lines go side to side
A diagonal line is slanted.
Write the expressions for (f x g) (x) and evaluate (f-g) (4)
The product and the sum of the functions will be 3x² - 6x - 24 and 4x + 2. The value of the function (f - g) at x = 4 is negative 18.
What is a function?In mathematics, functions are everywhere and are necessary for constructing physical connections. A function is a statement, rule, or law that establishes the connection between two variables.
The functions are given below.
f(x) = x - 4
g(x) = 3x + 6
Then the product of the functions will be
(f × g)(x) = (x - 4)(3x + 6)
(f × g)(x) = 3x² -12x + 6x - 24
(f × g)(x) = 3x² - 6x - 24
Then the sum of the functions will be
(f + g)(x) = x - 4 + 3x + 6
(f + g)(x) = 4x + 2
Then the difference in the functions at x = 4 will be
(f - g)(4) = (x - 4) - (3x + 6)
(f - g)(4) = x - 4 - 3x - 6
(f - g)(4) = -2x - 10
(f - g)(4) = -2 (4) - 10
(f - g)(4) = -8 -10
(f - g)(4) = -18
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anyone? giving brainliest to correct answer
Answer:
im not really sure what that means im so sorry
Step-by-step explanation:
write 615000 in scientific notation
Answer:
6.15 × 10⁵
Step-by-step explanation:
When converting a number of scientific notation, we need to move the decimal point until the number is greater than 1 and less than 10, then multiply this by 10 to the power of the number of places we moved the decimal point (negative when moving it forwards, positive when moving it backwards).
Therefore, 615000 = 6.15 × 10⁵
The length of a rectangle is four times its width.
If the perimeter of the rectangle is 60yd find it’s length and width
Answer:
Length = 24 yd
Width = 6 yd
Step-by-step explanation:
To start out, we can begin by saying that "l" is the length of the rectangle, and "w" is the width.
Since we know that the length (l) is 4 times its width we can say that 4 times the width is equal to its length. We would write this out this way :
4w = l
Next, we know that the perimeter is 60yd (as it is given in the question). We also know that the perimeter of a rectangle is all of its sides, added. Meaning the length plus the length, plus the width and the width. So, we can use the equation :
2l + 2w = p
"p" being the perimeter. And, since the perimeter is 60, we can place in 60 for "p"
2l + 2w = 60
Now we can use this information to combine the terms, and find the width and length. We first do this by noticing that in the first equation, it shows that "l" (the length) is equal to 4w. This means that we can put 4w in place of the "l" in the second equation. We can do this, becuase we know that "l" is equal to 4w. (from the first eqaution)
2 (4w) + 2w = 60
Now, we solve
2 * 4w = 8w
8w + 2w = 10w
So now we have :
10w = 60
To get the width, all we have to do is simply get "w" alone. We can do this by dividing both sides by 10.
10w = 60
/10 /10
w = 6
Therefore, the width is 6.
Now, going back to the first equaiton, we already know that the length is 4 times the width, meaning all we have to do is multiply 6 by 4 to get the length.
6 * 4 = 24.
Therefore, the length is 24.
Lastly, to check and make sure we are correct, we can go back to the second equation. 2l + 2w = 60
2 (24) + 2 (6) = 60
2 * 24 = 48
2 * 6 = 12
48 + 12 = 60
60 = 60
Now, we officially know that the length of the rectangle is 24 and the width is 6.
If A'B' is 8 find the length of AB.
If angle B is 40 degrees what is the measurement of B'?
If angle A is 80 degrees what is the measurement of A'?
Using AA what is the measurement of angle C?
The length of AB when A'B' is 8 is 12
The measurement of B' when angle B is 40° is also 40°
The measurement of A' when A is 80° is also 80°
The measurement of C using AB is 60°
What are similar triangles?Similar triangles are triangles that have the same angles and the ratio of their corresponding sides are equal.
Analysis:
ΔCA'B' is similar to ΔCAB.
Which means [tex]\frac{A'B'}{AB}[/tex] = [tex]\frac{CB'}{CB}[/tex] = [tex]\frac{CA'}{CA}[/tex]
A'B' = 8, CA' = 4, CA = 6
[tex]\frac{8}{AB}[/tex] = [tex]\frac{4}{6}[/tex]
4AB = 8 X 6
AB = 48/4 = 12
Line BA nd B'A' are parallel lines joined by two transversals BC and CA.
So, ∠B = ∠B' = 40°( corresponding angles are equal)
Also, ∠A = ∠A' = 80° ( corresponding angles are equal)
∠A + ∠B +∠C = 180( sum of angles in a triangle)
80 + 40 + ∠C = 180
120 + ∠C = 180
∠C = 180 - 120 = 60°
In conclusion,
The length of AB when A'B' is 8 is 12
The measurement of B' when angle B is 40° is also 40°
The measurement of A' when A is 80° is also 80°
The measurement of C using AB is 60°.
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As an event organizer, you are to host 120guests in a room of dimensions 18m long and 12m wide. You have rectangular tables which are 2m long and 0.75m wide. The number of guests allocated for the top table is 12 and the rest of the guests are on 3springs. NB: cover space is 0.6m i) Sketch the table plan arrangement. ii) Calculate the number of tables required for the top table. iii) Calculate the number of covers on each spring. iv) calculate the number of tables required for each spring. v) What is the purpose of leaving a gangway when arranging tables and chairs for an event?
The room, the tables and the guests are illustrations of rectangles and areas.
How many tables are required for the top table?This is calculated using:
Tables = Guest ÷ Guest per top table
So, we have:
Tables = 120 ÷ 12
Evaluate
Tables = 10
Hence, 10 tables are required for the top table
How many covers are on each spring?This is calculated using:
Covers = Number of spring ÷ Cover space
So, we have:
Covers = 3 ÷ 0.6
Evaluate
Covers = 5
Hence, 5 covers are required for each spring
How many tables are required for each spring?This is calculated using:
Tables = Tables for top table ÷ Spring
So, we have:
Tables = 10 ÷ 3
Evaluate
Tables = 3.33
Remove decimal
Tables = 3
Hence, 3 tables are required for each spring
What is the purpose of leaving a gangway when arranging tables and chairs for an event?This is done to allow passage for walkway
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To multiply 64 • 8.32, use the logarithmic equation:
1) log 72.32
2) log 64 + log 8.32
3) antilog 64 + antilog 8.32
4) (log 64)(log 8.32)
To multiply 64 × 8.32 use the logarithm equation 2)㏒64 + ㏒8.32
To answer the question, we need to know what logarithm of a number is
What is the logarithm of a number?The logarithm of a number x is the power to base 10 of that number.
So, logarithm of x to base 10 is written as ㏒x.
Since we want to multiply 64 × 83.2, we convert this to logarithmic equation using the addition rule of logarithm.
Addition rule of logarithm㏒ab = ㏒a + ㏒b
So, 64 × 8.32 to logarithm is ㏒(64 × 8.32) = ㏒64 + ㏒8.32
So, to multiply 64 × 8.32 use the logarithm equation 2)㏒64 + ㏒8.32
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What is the inverse of the function below?
f(x) = 3^x
---
OA 1-1(x) = logg
.
B. -() = log, 3
c. 1-2(1) = 3log(7)
D. 12() = log(31)
Original: y = 3^x
---To find the inverse, switch the x and y, then solve for y.
Inverse: x = 3^y
---Take the log base 3 of both sides to get y by itself
Answer: [tex]log_{3}(x) = y[/tex]
[tex]y = log_{3}(x)[/tex]
Hope this helps!
a. Lily paid $6 for 3/8 lb of nuts.
What is the unit rate as complex fraction (simplify)
Answer:
Ib = $16 per lb
Step-by-step explanation:
PLEASE HURRY
no links please
Stef rolls two six-sided number cubes. What is the probability that she rolls a 1 on
the first cube and a number greater than 1 on the second cube?
Use the diagram of
the sample space to help you.
A. 3/36 = 1/2
B. 5/36
C. 6/36 = 1/6
D. 1/36
please get this right because i might failll :(
Answer:
The answer is 5/36.
Step-by-step explanation:
Test approved.
The probability that she rolls a 1 on the first cube and a number greater than 1 on the second cube is 5/36.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
Given that Stef rolls two six-sided number cubes.
Based on the diagram of the sample space.
Therefore, the probability that she rolls a 1 on the first cube and a number greater than 1 on the second cube
= 5/36.
Hencce, the correct option is B.
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The composite figure shown is made up of 2 triangular prisms and one rectangular prism. If the area of each triangle base of the triangular prisms has an area of 24 m2, what is the total surface area of the composite figure? 120 m2 160 m2 760 m2 1,152 m2
The area of the composite figure is 1152 square meters
Complete QuestionA rectangular prism and 2 triangular prisms. The rectangular prism has a length of 20 meters, width of 6 meters, and height of 8 meters. The triangular prisms each have 2 triangular sides with a base of 6 meters and height of 8 meters. The rectangular sides are 20 meters by 6 meters, 20 meters by 10 meters, and 20 meters by 8 meters.
The composite figure shown is made up of 2 triangular prisms and one rectangular prism. If the area of each triangle base of the triangular prisms has an area of 24 m2, what is the total surface area of the composite figure?
How to determine the surface area?The given parameters are:
Rectangular prism :
Length = 20 meters; Width = 6 meters; Height = 8 meters
Triangular prism :
Triangular sides (2): Base = 6 meters; Height = 8 metersRectangular sides: 20 meters by 6 meters, 20 meters by 10 meters, and 20 meters by 8 meters.Base Area = 24 square meters:The area of the rectangular prism is:
Area = 2 * (Length * Width + Length * Height + Width * Height)
So, we have:
Area = 2 * (20 * 6 + 20 * 8 + 6 * 8)
Area = 656
The area of the triangular prism is:
Area = 2 * Base Area + Areas of Rectangular sides
So, we have:
Area = 2 * 24 + (20 * 6 + 20 * 10 + 20 * 8)
Area = 528
The common area between the prisms is:
Common area = 8 * 4
Common area = 32
Subtract the common area from the sum of the areas of the triangular prism and the rectangular prism to get the area of the composite figure
Composite figure = 656 + 528 - 32
Evaluate the sum
Composite figure = 1152
Hence, the area of the composite figure is 1152 square meters
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Answer: D, 1152 m2
Step-by-step explanation: I got it correct
Let $a_1, a_2, a_3, \dots$ be a non-constant arithmetic sequence. Suppose that $a_4, a_7, a_{12}$ form a geometric sequence. If $a_7 = 30$, what is $a_1$?
The terms a1, a2 and a3 do not have a common difference, and the value of a1 in the geometric sequence is 10/9
How to determine the value of the first term?The arithmetic sequence is given as:
a₁, a₂ and a₃
The geometric sequence is given as:
a₄, a₇ and a₁₂
The common ratio of a geometric sequence is:
[tex]r = \frac{T_2}{T_1}[/tex]
So,we have:
[tex]\frac{a_7}{a_4} = \frac{a_{12}}{a_7}[/tex]
Cross multiply
[tex]a_{12} * a_4 = a_7 * a_7[/tex]
Given that a7 = 30, the equation becomes
[tex]a_{12} * a_4 = 30 * 30[/tex]
Evaluate the product
[tex]a_{12} * a_4 = 900[/tex]
Rewrite as:
[tex]a_{4} * a_{12} = 900[/tex]
Express 900 as 10 * 90
[tex]a_{4} * a_{12} = 10 * 90[/tex]
By comparison, we have:
a₄ = 10 and a₁₂ = 90
This means that the geometric sequence is:
10, 30, 90 ---- it has a common ratio of 3
The nth term of a geometric sequence is:
[tex]a_n = ar^{n-1}[/tex]
So, we have:
[tex]a_7 = ar^6[/tex]
[tex]a_4 = ar^3[/tex]
Substitute values for a7 and 14
[tex]ar^6 = 30[/tex]
[tex]ar^4 = 10[/tex]
Divide both equations
[tex]r^2 = 3[/tex]
Take the cube of both sides
[tex]r^6 = 27[/tex]
Substitute [tex]r^6 = 27[/tex] in [tex]ar^6 = 30[/tex]
[tex]a * 27 = 30[/tex]
Divide both sides by 27
[tex]a = \frac{10}{9}[/tex]
Hence, the value of a1 in the geometric sequence is 10/9
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What is the value of the expression
1/2 divided by 6
Answer:
here is 1/2 divided displayed mathematically
1/2 ÷ 6
1= numerator
2= denominator
3= whole number
to make it fraction from the answer you keep the
numerator by the whole number to make a new
denominator
___1___ = _1_
2×6 12
thus the answer to 1/2 divided by 6 on fraction form is
1/12 is the answer
