Answer:
The inverse of the given function is [tex]$t(d)=\frac{d}{50}$[/tex]. The time taken to travel 180 miles is 3.6 hours.
Step-by-step explanation:
It is given that a car travels at a constant speed of 50 miles per hour. A function for distance traveled is also given as d(t)=50t.
It is required to find the inverse of the function by expressing the time travel in terms of distance traveled and also find t(180).
To find the inverse, express time traveled in terms of distance traveled using normal algebraic methods and then substitute 180 for t and explain its results.
Step 1 of 2
The given function is d(t)=50t.
Consider d(t) as d and t as t(d) and rewrite the equation.
The rewritten function is d=50 t(d)
Divide by 50 on both sides of the equation.
[tex]$$\begin{aligned}&d=50 t(d) \\&\frac{d}{50}=\frac{50 t(d)}{50} \\&t(d)=\frac{d}{50}\end{aligned}$$[/tex]
Step 2 of 2
Substitute 180 for $t$ in the simplified expression and interpret the results.
[tex]$$\begin{aligned}&t(d)=\frac{d}{50} \\&t(d)=\frac{180}{50} \\&t(d)=3.6\end{aligned}$$[/tex]
The time taken to travel 180 miles is 3.6 hours.
5. How many 6-digit numbers can be formed from the digits 0,1,3,5,7 and 9 which are divisible by 10 and no digit is repeated?
There are 120 6-digit numbers that can be formed
How to determine the combination of digits?The digits are given as:
0,1,3,5,7 and 9
Since the number must be divisible by 10.
Then the number must end in 0
The other 5 digits can take any of the 0,1,3,5,7.
So, the number of combination is:
Count = 5! * 1
Expand
Count = 5 * 4 * 3 *2 * 1 * 1
Evaluate
Count = 120
Hence, there are 120 6-digit numbers that can be formed
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What is the solution of the equation (x – 5)2 3(x – 5) 9 = 0? use u substitution and the quadratic formula to solve.
The value of x in the equation [tex](x-5)^{2} +3(x-5)+9=0[/tex]is x=(7+3[tex]\sqrt{3}i[/tex])/2,
(7-3[tex]\sqrt{3}i[/tex])/2.
Given equation [tex](x-5)^{2} +3(x-5)+9=0[/tex] .
We have to find the solution of the equation.
Equation is solved to find the value of variables. The number of values of the variable depends on the highest power of variables.
let (x-5)=u-------------------1
equation becomes [tex]u^{2} +3u+9=0[/tex]
solution of a quadratic formula
x=-b±[tex]\sqrt{b^{2} -4ac}[/tex]/2a
on comparing with general form a=1,b=3, c=9
u=-3±[tex]\sqrt{3^{2} -4*1*9} /2[/tex]
=-3±[tex]\sqrt{9-36}/2[/tex]
=-3±[tex]3\sqrt{-27}/2[/tex]
=-3±[tex]3\sqrt{3} i/2[/tex]
[tex]u_{1} =-3[/tex]+3[tex]\sqrt{3}/2[/tex] , [tex]u_{2}[/tex]=-3-3[tex]\sqrt{3}/2[/tex]
put the values of [tex]u_{1}[/tex] in equation 1
x-5=[tex]u_{1}[/tex]
x-5=-3+[tex]3\sqrt{3} /2[/tex]
x=-3+3[tex]\sqrt{3}i/2+5[/tex]
x=7+3[tex]\sqrt{3} i/2[/tex]
put the values of [tex]u_{2}[/tex] in equation2
x-5=[tex]u_{2}[/tex]
x-5=-3-3[tex]\sqrt{3} /2[/tex]
x=7-3[tex]\sqrt{3}/2[/tex]
Hence the values of x are 7+3[tex]\sqrt{3}i/2[/tex], 7-3[tex]\sqrt{3}i/2[/tex].
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A scuba diver is 50 ft below sea level. Which of the following best describes this situation?
1. |50|
2. -50
3. +50
4. ±50
Answer:
-50
Explanation:
At sea level would be 0 so anything above would be a positive number and anything below a negative number.
What is the difference? −9 4/5−(−3 2/3)
Subtraction is a mathematical operation that reflects the removal of things from a collection. The difference between −9 4/5 and −3 2/3 is -6 2/15.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
The difference between −9 4/5 and −3 2/3 is,
−9 4/5 − (−3 2/3)
= −9 4/5 + 3 2/3
= (−9+3) + (−4/5 + 2/3)
= −6 + (-2/15)
= -6 2/15
Hence, The difference between −9 4/5 and −3 2/3 is -6 2/15.
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The sum of two numbers is 79. Three
times the first number added to 5 times
the second number is 283. What are the
two numbers?
Answer:
The two numbers are 23 and 56
Step-by-step explanation:
Let's say the two numbers are A and B.
We are told:
1) A+B=79
2) 3A+5B=283
Let's take the first expression and solve for A:
A+B=79
A=79-B
Now use this value of A in the second expression:
3A+5B=283
3(79-B)+5B=283
237-3B+5B=283
2B = 46
B = 23
Since B=23, we know from 1) that
A+B=79
A+23=79
A = 56
CHECK:
Does A+B=79?
56+23 = 79? YES
Does 3A+5B=283?
3(56)+5(23)=283
168 + 115 = 283? YES
a nunebr is chosen at random from 1 to 50 find the probability of selecting numbers greater than 30 and less than 45
Answer:
7/25
Step-by-step explanation:
there are 14 numbers greater than 30 and less than 45
31 32 33 34 ......42 43 44 <=====14 numbers
14 choices out of 50 = 14/ 50 = 7/25
Which ordered pair is a solution of the equation 3x + y = 15?
Answer: 3(3)+6=15
Step-by-step explanation:
X=3 and the Y=6
( ) means multiplying so it 3 multiplied (3) and add 6 which Is the Y then you got the answer which is 15.
A toy manufacturer wants to know how many new toys children buy each year. A sample of 1492 children was taken to study their purchasing habits. Construct the 99% confidence interval for the mean number of toys purchased each year if the sample mean was found to be 8.8. Assume that the population standard deviation is 2.2. Round your answers to one decimal place.
By assuming the standard deviation of population 2.2 the confidence interval is 8.67 toys,8.94 toys.
Given sample size of 1492 children,99% confidence interval , sample mean of 8.8, population standard deviation=2.2.
This type of problems can be solved through z test and in z test we have to first find the z score and then p value from normal distribution table.
First we have to find the value of α which can be calculated as under:
α=(1-0.99)/2=0.005
p=1-0.005=0.995
corresponding z value will be 2.575 for p=0.995 .
Margin of error=z*x/d
where x is mean and d is standard deviation.
M=2.575*2.2/[tex]\sqrt{1492}[/tex]
=0.14
So the lower value will be x-M
=8.8-0.14
=8.66
=8.67 ( after rounding)
The upper value will be x+M
=8.8+0.14
=8.94
Hence the confidence interval will be 8.67 toys and 8.94 toys.
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The area of a rectangle is 59.5 square inches. The base of the
rectangle is 7 inches.
What is the height of the rectangle, in inches?
O A. x = 52.5 in
OB. x = 8.5 in
OC. x= 416.5 in
OD. x= 22.75 in
Answer:
Step-by-step explanation:
Givens
Area = 59.5 in^2
Base = 7 inches
height = h
Solution
Area = Base * height Substitute what you know in the formula
59.5 = 7 * h Divide both sides by 7
59.5/7 = 7h / 7
h = 8.5
Answer height = 8.5
Answer:
Answer B is correct
Step-by-step explanation:
The formula to find the area of a rectangle is :
Area = Base × Height
Given that,
Area ⇒ 59.5 in²
Base ⇒ 7 in
Height ⇒?
Let the height of the rectangle be x.
First, let us make an expression to find the value of h.
Area = Base × Height
59.5 = 7 × x
And now let us solve for x.
59.5 = 7h
Divide both sides by 7.
x = 8.5 in
help me please 10 points!!
Answer:
104m²
Step-by-step explanation:
we can find the area of a trapezoid from its bases and height in the following formula:
[tex]A=\frac{a + b}{2}h[/tex]
where...
A: area
a: one base
b: other base
h: height
here, we can see that our two bases are 9 and 17, and that our height is 8.
Now, let's plug these values into our formula:
a: 9
b: 17
h: 8
[tex]A=\frac{a + b}{2}h[/tex]
[tex]A=\frac{9 + 17}{2}8[/tex]
Now, we can simplify:
[tex]A=\frac{9 + 17}{2}8[/tex]
[tex]A=\frac{26}{2}8[/tex]
A = 13 · 8
A = 104
so, the area of this trapezoid is 104m²
(note: we write area as squared / in square units)
hope this helps! have a lovely day :)
5.
AMNOP is a square-based pyramid where the volume of pyramid is
392 cm³ and the height is 6 cm. Find the each side of the base area of pyramid.
The length of each side of the base of the pyramid is 14 cm
Volume of a pyramidFrom the question, we are to determine the length of each side of the base of the pyramid
The volume of a square-based pyramid is given by
V = 1/3(b²h)
Where V is the volume
b is the length of the base
and h is the height
From the given information,
V = 392 cm³
h = 6 cm
Putting the parameters into the equation, we get
392 = 1/3(b²× 6)
392 = b² ×2
b² = 392/2
b² = 196
b = √196
b = 14 cm
Hence, the length of each side of the base of the pyramid is 14 cm
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Given that (7-2x),9,(5x+17) are consecutive terms of a geometric progression with common ratio, r>0, find the value of x.
This are also referred to as exponential sequence. The common ratio if r > 0 is 2
Geometric sequenceThis are also referred to as exponential sequence. Given the following sequence
(7-2x),9,(5x+17)
If they are in geometric progression, hence;
9/7-2x = 5x+17/9
Cross multiply
7-2x(5x+17) = 9(9)
Expand
35x+119-10x²-34x = 81
-10x²+x+119-81=0
10x²-x-38 = 0
Factorize
10x²-20x +19x-38 = 0
10x(x-2)+19(x-2)= 0
x - 2 = 0
x = 2
Hence the common ratio if r > 0 is 2
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PLEASE HELP! You are covering the metal wedge below with a thin layer of high-conducting silver (surface area). The measurements shown are in centimeters. Find the cost of covering the wedge in silver, if silver plating costs $3 for every 2 square centimeters.
The cost of covering the triangular prism wedge in silver is: $108.
What is the Surface Area of a Triangular Prism?Surface area = (s1 + s2 + s3)L + bh.
Given the following:
s1 = 10s2 = 8s3 = 6L = 0.5b = 6 h = 8Plug in the values into the formula
Surface area of the triangular prism metal wedge = (10 + 8 + 6)0.5 + (6)(8)
Surface area of the triangular prism metal wedge = 72 cm²
Cost of covering = 72/2 × 3 = $108
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Given the system
4x + 2y 2z = 10 (A)
2x + 8y + 4z = 32 (B)
30x+12y - 4z = 24 (C)
The values of the variables are x = -2, y = 6 and z = -3
How to solve by elimination?The system is given as:
4x + 2y - 2z = 10 (A)
2x + 8y + 4z = 32 (B)
30x + 12y - 4z = 24 (C)
The easiest variable to eliminate is z.
Combine A and B
2[4x + 2y - 2z = 10]
⇒
8x + 4y - 4z = 20
+ 2x + 8y + 4z = 32
⇒ 10x + 12y = 52
Combine B and C
2x + 8y + 4z = 32
30x + 12y - 4z = 24
⇒ 32x + 20y = 56
Divide through by 4
8x + 5y = 14
So, we have:
10x + 12y = 52
and
8x + 5y = 14
Multiply 10x + 12y = 52 by 8/10
8/10[10x + 12y = 52]
⇒ 8x + 9.6y = 41.6
Combine 8x + 9.6y = 41.6 and 8x + 5y = 14
8x + 9.6y = 41.6
- [8x + 5y = 14]
⇒ 4.6y = 27.6
Divide
y = 6
Substitute y = 6 in 8x + 5y = 14
8x + 5 * 6 = 14
8x + 30 = 14
Subtract 30
8x = -16
Divide
x = -2
Substitute y = 6 and x = -2 in (A)
4x + 2y - 2z = 10
4(-2) + 2(6) - 2z = 10
-8 + 12- 2z = 10
Evaluate the like terms
-2z = 6
Divide
z = -3
Hence. the values of the variables are x = -2, y = 6 and z = -3
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Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial x²-x-6
Zeros of this function
x²-x-6=0x²-3x+2x-6=0x(x-3)+2(x-3)=0(x+2)(x-3)=0x={-2,3}ZEros of reciprocal function
x={-1/2,1/3}The equation
x²-(-1/2+1/3)x-(1/2)(1/3)=0x²-1/6x-1/6=0cChoose all that apply. If a population is decreasing in size, you would expect lambda to be ___________________ and r to be _______________________.
If the population can be shown to be decreasing in size, then the lambda would be positive while the r would be negative.
What happens when the population is decreasing?When the population is decreasing, the rate would be negative because the population is shrinking. This is why r - which is rate - will be negative.
Lambda on the other hand will be positive to show that the population started from a higher value and is now decreasing.
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I need help asap with thissssssssssss
Answer:
D
Step-by-step explanation:
The domain is the x value which in this case would be the hours of training
HELPS I NEED THE ANSWER PLSSSSSSSSSSSS!
Answer:
5.5x+7.146 (the six is repeating)
Step-by-step explanation:
Answer:
5.5x + 7.25
Step-by-step explanation:
5.5(x+6.5)-(x+9.5)-(19-x) Convert the fractions to decimal
5.5x+35.75 -x - 9.5 - 19 +x Expand
(5.5x - x + x) +(35.75 - 9.5 - 19) Group like terms
5.5x + 7.25 Combine like terms
turn y=6x-5 (explicit) into a recursive equation
Answer:
[tex]a_1=1\\a_n=a_{n-1}+6[/tex]
Step-by-step explanation:
So to define a recursive equation, you need to find how much each term is increasing or decreasing by. You also need to find the first term. To find the first term you can simply plug in 1 into x: [tex]a_1=6(1)-5 = 6-5 = 1[/tex]. And as you can see the slope is 6, so each term is increasing by 6. So you get the recursive function: [tex]a_1=1\\a_n=a_{n-1}+6[/tex]
What is tan 30°?
1
60
90°
√3
2
30⁰
OA. √2
OB.
O C.
O D.
√√3
√√3
OE. √3
O F. 1
Answer: [tex]\frac{\sqrt{3}}{3}[/tex]
Step-by-step explanation:
[tex]\tan 30^{\circ}=\frac{\sin 30^{\circ}}{\cos 30^{\circ}}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}[/tex]
The value of the trigonometric relation tan 30° = 1/√3
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the trigonometric relation be represented as A
Now , the value of A is
A = tan 30°
And , tan θ = sin θ / cos θ
On simplifying , we get
sin 30° = 1/2
cos 30° = √3/2
Substituting the values in the equation , we get
tan 30° = sin 30° / cos 30°
tan 30° = ( 1/2 ) / ( √3/2 )
tan 30° = 1/√3
Hence , the value of relation tan 30° is 1/√3
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How many solutions does this system have?
x+4y=6
y=2x-3
Oone
Otwo
Oan infinite number
Ono solution
Pls I need help
Answer:
-x+3y=9
i think this is answer
URGENT PLEASE ANSWER THESE ASAP
Answer:
(b) 25 muffins
(c) 38 muffins
Step-by-step explanation:
Given:
A cookie cost $0.80 A muffin costs $1.60buy 200 treatsspend $200 or lessForming system of linear equations:
muffins (m) + cookies (c) = 200 treats
1.60m + 0.80c = $200
Solve by Substitution:
m + c = 200
1.6m + 0.8c = 200
using m + c = 200, solve for m by subtracting c:
m + c - c = 200 - c
m = 200 - c
we can now plug in m tot he second equation,
1.6(200 - c) + 0.8c = 200
320 - 0.8c = 200
320 - 320 - 0.8c = 200 - 320
-0.8c = -120
-0.8c/-0.8 = -120/-0.8
c = 150
plug c back in to find m,
m = 200 - c
m = 200 - 150
m = 50
(b) if you buy 200 cookies, then how many muffins?
we use this equation as we want to stay in the price limit: 1.6m + 0.8c = 200
c = 200 so 1.6m + 0.8(200) = 200
1.6m + 0.8(200) = 200
1.6m + 160 = 200
1.6m = 200 - 160
1.6m = 40
1.6m/1.6 = 40/1.6
m = 25
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Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
556. 0.00000871
Answer:
Hence, 0.0000087 can be expressed as [tex]$8.71 \times 10^{-6}$[/tex].
Step-by-step explanation:
- Given 0.00000871
- Move the decimal point so that the factor is greater than or equal to 1 but less than 10 .
- Then count n and write no. as product with a power of 10 .
Step 1 of 1
Consider 0.00000871,
8.71
Decimal has moved 6 places to right.
The power will be negative as the original no. is less than 1 .
[tex]$$\begin{array}{r}8.71 \times 10^{-6} \\0.0000087=8.71 \times 10^{-6}\end{array}$$[/tex]
(b) In the figure, AABC and ACDE are equilateral triangles. Prove that: AD = BE.
i have sent the picture of the figure also please send the solution fast
Since both the given triangles are equilateral, their interior angles are each measure 60°.
Consider triangles ADC and BEC.
We have:
AC = BC (given)DC = EC (given)ACD = ACB + BCD = 60 + BCD (angle addition)ECB = ECD + BCD = 60 + BCD (angle addition)According to above, two sides and the included angle of triangles ADC and BEC are congruent by ASA.
Therefore AD = BE as corresponding sides of congruent triangles, hence proved.
12(x + 4) + 8 = 9
y = 4(x + 4)
y=
Answer:
y= 1/3
Step-by-step explanation:
12(x + 4) + 8 = 9
12(x + 4) + 8 -8 = 9 -8
12(x + 4) = 1
12(x + 4)/12 = 1/12
(x + 4) = 1/12
y = 4(x + 4)
y= 4(1/12)
y= 4/12
y= 1/3
Which of the following properly describe "slope"? Select all that apply.
Y₂
x₂-x
0
x₂7x
y₂-yi
Orun / rise
Orise / run
Oratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run)
Answer:
I would assume you're referring to this test? if so the answer is
a, d and e
The expression that describes the slope properly are:
A. m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
D. m = rise/run
E. Ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run).
We have,
The slope of a line is a measure of its steepness or inclination.
It represents the rate of change between two points on the line, specifically the ratio of the vertical change (rise) to the horizontal change (run).
Mathematically, the slope (m) is calculated as:
m = change in vertical distance/change in horizontal distance
or
m = rise/run
or
m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Thus,
The expression that describes the slope properly are:
A. m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
D. m = rise/run
E. Ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run).
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Suppose you have a valid argument with a false conclusion. Given this information, what do you know about the truth value of the argument's premises? The premises must all be false. At least one premise must be false. There must be at least one true premise and at least one false premise. The premises may be any combination of true and false. The premises must all be true.
Suppose you have a valid argument with a false conclusion. Given this information, what do you know about the truth value of the argument's premises? The premises must all be false. At least one premise must be false. There must be at least one true premise and at least one false premise. The premises may be any combination of true and false. The premises must all be true.
"The argument may be either valid or invalid" When trying to determine the validity of an argument in logic, the truth of a premise is a non-factor. Logic is concerned about whether or not an argument would effectively transfer truth from its premises to the conclusion if the premises were true.
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In an election, 1200 total votes were cast for the 3 candidates. The second-place candidate received 155 fewer votes than the winner and 200 votes more than the third-place candidate. How many votes did the winner receive
The winner received 570 votes.
Let the winner candidate be c1
Let the second-place candidate be c2
Let the third-place candidate be c3
[tex]c2=c1-155\\[/tex].........equation 1
[tex]c2=c3+200\\[/tex]
[tex]c3=c2-200 \\[/tex]
[tex]c3=c1-155-200\\[/tex].........by equation 1
[tex]c3=c1-355[/tex]........equation 2
Now we know,
[tex]c1+c2+c3=1200[/tex]
[tex]c1+(c1-155)+(c1-355)=1200[/tex] .....by equations 1 and 2
[tex]3c1-510=1200[/tex]
[tex]3c1=1200+510\\3c1=170\\c1=570[/tex]
Hence, The winner received 570 votes.
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If my savings of $x grows 10% each year, how much will I have in 2 years?
Answer:
1.21x
Step-by-step explanation:
we can write 100% as 1
then 10% is 0.1
then 1.1x = is first
1.1*1.1x = 1.21x or 121% of x
The savings of $x grows 10% each year after 2 year it will become 1.21x .
What is compound interest?Compound interest is an interest accumulated on the principal and interest together over a given time period. The interest accumulated on a principal over a period of time is also accounted under the principal.
The formula of Compound interest :
[tex]A= P(1+\frac{r}{100} )^{t}[/tex]
where,
A = Final amount
P = initial Principal
t = Time in years
r = rate of interest per annum
According to the question
Principal = $x
Rate of interest per annum = 10%
Time in years = t
By using formula of Compound interest :
[tex]A= P(1+\frac{r}{100} )^{t}[/tex]
Now ,
Substituting the values in the formula
[tex]A= x(1+\frac{10}{100} )^{2}[/tex]
[tex]A= x(1.1} )^{2}[/tex]
[tex]A= 1.21x[/tex]
Hence, the savings of $x grows 10% each year after 2 year it will become 1.21x .
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Can someone please help
Answer: 2.5
Step-by-step explanation:
[tex]1 \times 3=3\\\\3-\frac{1}{2}=2.5[/tex]