By taking the quotient between distance and time, we conclude that her speed is 108.8 miles per hour.
How to find her speed?
Here we will use the next relation:
speed = distance/time.
Here we know that Mackenzie drove 68 miles in (1 + 3/5) hours, then:
distance = 68 mi
time = (1 + 3/5) hours = (8/5) hours.
Then the speed will be:
speed = 68mi/(8/5) hours. = 68*(8/5) mi/h = 108.8 mi/h
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Find all solutions of the equation in the interval [0,2pi). csc =7/4 If there is more than one solution, separate them with commas.Do not round any intermediate computations. Give your answer(s) in radians, and round your answer(s) to the nearest hundredth
Since the cosecant is the inverse of the sine, we can write the following:
[tex]\begin{gathered} \csc (\theta)=\frac{7}{4} \\ \sin (\theta)=\frac{1}{\csc(\theta)}=\frac{1}{\frac{7}{4}}=\frac{4}{7} \end{gathered}[/tex]Then, using a calculator, we can calculate the angle that has a sine of 4/7:
[tex]\begin{gathered} \theta=\sin ^{-1}(\frac{4}{7})_{} \\ \theta=34.85\degree \end{gathered}[/tex]There is one more angle between 0 and 2π that has the same value of 4/7 for the sine, and it's the supplementary angle to the one we found:
[tex]\theta_2=180-\theta_1=180-34.85=145.15\degree[/tex]Therefore the answers are 34.85° and 145.15°.
Converting to radians, we have:
[tex]\begin{gathered} 34.85\cdot\frac{\pi}{180}=0.61 \\ 145.15\cdot\frac{\pi}{180}=2.53 \end{gathered}[/tex]So the final answer is 0.61 and 2.53.
1. what is the area of the board shown on the scale drawing? explain how you found the area.2. how can Adam use the scale factor to find the area of the actual electronics board? remember, he uses a different method than Jason.3. what is the area of the actual electronics board?
Answer:
1. 1800 square cm.
2. See below
3. 45000 square cm.
Explanation:
Part 1
The dimensions of the drawing are 36cm by 50cm.
[tex]\begin{gathered} \text{The area of the board}=36\times50 \\ =1800\operatorname{cm}^2 \end{gathered}[/tex]Part 2
Given a scale factor, k
If the area of the scale drawing is A; then we can find the area of the actual board by multiplying the area of the scale drawing by the square of k.
Part 3
[tex]\begin{gathered} \text{Area of the scale drawing}=1800\operatorname{cm}^2 \\ \text{Scale Factor,k=5} \end{gathered}[/tex]Therefore, the area of the actual drawing will be:
[tex]\begin{gathered} 1800\times5^2 \\ =45,000\operatorname{cm}^2 \end{gathered}[/tex]what does this mean i dont get it please help me thanks, :)
It means that you are supposed to group The like terms together and simplify them
you will find that 2t is the liketerm with -5t and -u is a like term with -6u
As a results we have
[tex] = 2t - 5t - u - 6u \\ = - 3t - 7u[/tex]
as indicated I have shown you the answer .
good luck
Two lines are shown on the grid below.Read the statements below about the graph of the two lines.Which statements are true about the two lines on the graph?A.I,II, and IV onlyB.II,III, and IV onlyC.II and III only D.I,II,III,and IV
Answer:
B. II, III, and IV only
Explanation:
Vertical lines have an undefined slope and the equation of these lines is x = c, where c is a constant value
Horizontal lines have a slope equal to 0 and the equation of these lines is y = c, where c is a constant value.
Therefore, the statements that are true about the graph are:
The equation of line b is y = -5
Line b has a slope of 0
The equation of line a is x = 3
Complete the table for y=-3x + 5 and graph the resulting line. -
We fill the table as follows:
*We assign values for x and solve for y, that is:
*x = 0:
[tex]y=-3(0)+5\Rightarrow y=5[/tex]So, the value of y when x = 0 is 5.
*x = 1:
[tex]y=-3(1)+5\Rightarrow y=2[/tex]So, the value of y when x = 1 is 2.
*x = 2:
[tex]y=-3(2)+5\Rightarrow y=-1[/tex]So, the value of y when x = 2 is -1.
*x = 3:
[tex]y=-3(3)+5\Rightarrow y=-4[/tex]So, the value of y when x = 3 is -4.
***The table should look like this:
x | y
0 | 5
1 | 2
2 | -1
3 | -4
***The graph is:
Which phrase represents this expression?
5 + 4 ÷ 2
Responses
the product of 5 and the quotient of 4 and 2
the product of 5 and the quotient of 4 and 2
the product of 5 and 4 is divided by 2
the product of 5 and 4 is divided by 2
the sum of 5 and 4 is divided by 2
the sum of 5 and 4 is divided by 2
the sum of 5 and the quotient of 4 and 2
On a 7 question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?Give your answer as a fraction
Solution
- This is a Binomial probability question. The formula for Binomial probability is:
[tex]\begin{gathered} P(r)=\sum\text{ }^nC_rp^rq^{n-r} \\ where, \\ n=The\text{ total number of trials} \\ r=\text{ The number of successful trials\lparen where answer is correct\rparen} \\ p=\text{ The probability of success \lparen The probability of getting a question } \\ right) \end{gathered}[/tex]- We have been given:
[tex]\begin{gathered} n=7 \\ \text{ since there can only be two answers, it means that the} \\ \text{ probability of getting a question correct is:} \\ p=\frac{1}{2} \\ q=1-p=\frac{1}{2} \\ \\ \text{ The probability of getting at least 1 question wrong means the } \\ probability\text{ of getting 1, 2, 3, 4, 5, 6, or 7 question wrong.} \\ \\ \text{ Instead of calculating all these probabilities, we can simply say} \\ P(1)+P(2)+P(3)+P(4)+P(5)+P(6)+P(7)=1-P(0) \end{gathered}[/tex]- Thus, we have:
[tex]\begin{gathered} P(0)=^7C_0(\frac{1}{2})^0(\frac{1}{2})^7 \\ P(0)=\frac{1}{128} \\ \\ 1-P(0)=1-\frac{1}{128}=\frac{127}{128} \end{gathered}[/tex]Final Answer
The answer is
[tex]\frac{127}{128}[/tex]A 14 m long ladder is placed against a tree. The top of the ladder reaches a point
13 m up the tree.
How far away is the base of the ladder from the base of the tree?
Give your answer in metres (m) to 1 d.p.
Answer:
Approximately 5.2 meters
Step-by-step explanation:
This formation will make a right triangle. The ground to the point in the tree is one of the legs. The base of the tree to the base of ladder is another leg and the length of the ladder is the hypotenuse. In this case, we already have the hypotenuse and one of the legs, so we need to find the value of another leg.
We can do so by using the Pythagorean Theorem which is [tex]a^2+b^2=c^2\\[/tex].
a and b represent the values of the two legs, and c is the hypotenuse. Since we already have the hypotenuse, we can change this equation a bit to find the other leg.
Let's assign the missing value, b in the theorem.
The new equation will be [tex]b^2=c^2-a^2[/tex].
We can insert the values for c and a and solve for b.
The new equation will be [tex]b^2 = 14^2-13^2[/tex].
[tex]b^2=196-169[/tex]
[tex]b^2=27[/tex]
[tex]\sqrt{b^2} =\sqrt{27}[/tex]
The square root of [tex]b^2[/tex] cancels out.
The approximate square root of 27 is 5.19 which we can round to 5.2.
Function g is a transformation of the parent function exponential function. Which statements are true about function g?
For the given function, The following are true statements:
Four units separate function g from function f.There is a y-intercept for function g. (0,4)Function g has a range of (3,∞ ).Over the range (-, ∞), function g is positive.It may be seen from the graph below that
The g function's graph is 4 units higher than the parent exponential function's graph.
All of the input values for which the function is defined are referred to as the function's domain. The domain of the function is (-, ∞ ) according to the graph of function g.
The location where a function's graph crosses the y-axis is known as the y-intercept. G's graph crosses the y-axis at (0, 4). As a result, the Function g's y-intercept is (0,4).
growing function g across the range (- ∞, 0).
Function output values are referred to as the function's range. It can be seen from the graph that the range of function g is (3, ∞ ).
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A 33-inch piece of steel is cut into three pieces so that the second piece is twiceas long as the first piece, and the third piece is one inch more than five times thelength of the first piece. What is the length of the first piece?
Let;
x = the length of the first piece
y=the length of the second piece
z=the length of the third piece
From the question;
"the second piece is twice as long as the first piece" can be written in equation as:
y = 2x
"the third piece is one inch more than five times the length of the first piece"
can be written as :
z= 5x+ 1
Total length of the 3 pieces = 33
This implies:
x + y + z =33
substitute y=2x and z=5x+1 into the above
x + 2x + 5x+1 = 33
8x + 1 = 33
subtract 1 from both-side of the equation
8x = 33 -1
8x = 32
divide both-side of the equation by 8
x= 32/8
x= 4
The length of the first piece is 4-inches
6) Write the equation of the line, in point-slope form, that passes through the point (-2,5) and has a slopeof 3.
Write the equation of the line, in point-slope form, that passes through the point (-2,5) and has a slope
of 3
___________________________________________________
The point-slope form
y-y1 = m (x-x1)
The slope (m)= 3
The point (x1, y1) = (-2,5)
____________
Replacing
y-5 =3 (x- (-2))
_______________
Answer
(y-5) =3 (x +2)
Do you have any questions regarding the solution?
Figure RSTU has coordinates R = (3,4), S = (7.2), T = (5, 10), and U = (12,8). The figure is dilated from the origin by a scale factor r . Select the correct coordinates of R. A R' = (3,2) B R' = (1.5, 4) C R' = (3.5, 4.5) D R' = (1.5, 2) * Select the correct answer. 1 point Ο Α OB D
Answer
Option D is correct.
R' (1.5, 2)
Explanation
A dilation means the size is increased or decreased. If the scale factor is less than 1, then the size is decreased, but if the scale factor is more than 1, it means the figure is enlarged.
Dilating about the origin just multiplies the coordinates by the scale factor. So, dilating (x, y) about the origin by a scale factor k, gives new coordinates (kx, ky).
For this question, we need to dilate R (3, 4) by a scale factor, r = ½
R' = [½(3), ½(4)] = (1.5, 2)
Hope this Helps!!!
A toy car that is 0.5 ft long is used to model the actions of an actual car that is 15 ft long. Which ratio shows the relationship between the sizes of the model and the actual car? A. 2:5 B. 5:2 C. 30:1 D. 1:30
A toy car that is 0.5 ft long is used to model the actions of an actual car that is 15 ft long. Which ratio shows the relationship between the sizes of the model and the actual car?
A. 2:5
B. 5:2
C. 30:1
D. 1:30
_____________________
0.5 ft the toy car: 15 the actual car
0.5*2 =1
15 *2 = 30
1: 30
_____________________________________
The ratio1:30 shows the relationship between the sizes of the model and the actual car
____________
Do you have any questions regarding the solution?
What is the measure of ?ХvO A. 46°42°42"38°NуvO B. 42°O C. 40°O D. 38°
The value Z is denoted as the center of the circle. Therefore, arc UV and arc XY should be the same .
[tex]undefined[/tex]Answer: A. 42°
Step-by-step explanation:
Hope this helps :)
The height of a pole is 15 feet. A line with banners is connected to the top of the poleto a point that is 8 feet from the base of the pole on the ground. How long would theline with banners need to be in order for the pole to be at a 90° angle with the ground?Explain your reasoning.
In order to have a 90º angle (right angle) the length of the line with banners needs to fullfit the Pythagorean theorem: In a right triangle the squared hypotenuse is equal to the sum of the legs squared:
[tex]h^2=l^2+l^2[/tex]In the given situation the hypotenusa is the line with banners, and the legs are the pole and the 8ft ground from the base of the pole to the end of the line with banners:
h= x
l= 15ft
l= 8ft
[tex]x^2=(15ft)^2+(8ft)^2[/tex]Solve the equation to find the value of x:
[tex]\begin{gathered} x^2=225ft^2+64ft^2 \\ x^2=289ft^2 \\ x=\sqrt[]{289ft^2} \\ x=17ft \end{gathered}[/tex]Then, to make a right triangle the length of the line witg banners need to be 17ftuse and show all conversion factors to convert 352 inches per second to miles per hour. 352 inches divided by 1 second
Okay, here we have this:
We need to convert 352 inches per second to miles per hour. So we obtain the following:
[tex]\begin{gathered} \frac{352in}{1sc}\cdot\frac{1mile}{63360in}\cdot\frac{3600sc}{1h} \\ =\frac{20\text{miles}}{h} \end{gathered}[/tex]Finally we obtain that 352 inches per second 20 are miles per hour.
Hi, can you help me to solve this problem please!
We have the following function
[tex]f(x)=7+6x[/tex]Now, we must replace the variable x by the given value, that is,
[tex]f(10)=7+6(10)[/tex]which gives
[tex]\begin{gathered} f(10)=7+60 \\ f(10)=67 \end{gathered}[/tex]Therefore, the answer is f(10)=67
Solve each equation for the variable. h/2 + 3.5 = 7.1
To answer this question, we can proceed as follows:
[tex]\frac{h}{2}+3.5=7.1[/tex]1. Subtract 3.5 to both sides of the equation:
[tex]\frac{h}{2}+3.5-3.5=7.1-3.5\Rightarrow\frac{h}{2}+0=3.6[/tex]2. Multiply by 2 to both sides of the equation:
[tex]2\cdot\frac{h}{2}=2\cdot3.6\Rightarrow h=7.2[/tex]We can check this result as follows:
[tex]\frac{7.2}{2}+3.5=3.6+3.5=7.1\Rightarrow7.1=7.1[/tex]This result is TRUE. Then, the value for h = 7.2.
2000.5 - 351.748 +62.1
Given the expression :
[tex]2000.5-351.748+62.1[/tex]At first make all the decimal digits equally for all terms
The maximum decimal is 3 so, add 00 to the first and the last terms
So,
[tex]\begin{gathered} 2000.5-351.748+62.1 \\ =2000.500-351.748+62.100 \\ =1710.852 \end{gathered}[/tex]So, the answer is : 1,710.852
Explain how you know 437,160 is greater than 43,716.4 grade student
437,160 is read as four hundred thirty-seven thousand one hundred sixty and 43,716 is read as fourty-three thousand seven hundred sixteen.
The first number has hundreds of thousand and the second one only has tens of thousand. It means that the first number is greater than the second one.
Another way to know this is because of the number of figures before the decimal point. The first number has 6 figures before the decimal point and the second one only has 5.
That way, we know that 437,160 is greater than 43,716.
find the x value (6x+9)° (4x-19)°
In this problem m and n are parallel lines, and the first angle is an exteriar angle an the secon is a interior angle.
this two condition give us that the two angles are complementary anlges so the sum of them should be 180 so:
[tex]6x+9+4x-19=180[/tex]and we can solve for x so:
[tex]\begin{gathered} 10x-10=180 \\ 10x=180+10 \\ x=\frac{190}{10} \\ x=19 \end{gathered}[/tex]helppppppppppppppppppppppppppp
Step-by-step explanation:
make the fractions decimals and put them on the plot
X+87°2x⁰ i have to solve for x it’s a 180 angle HELP ME!!!!!!!!!
b. Write
√x
as a single radical in simplest form.
5√x
Answer:
(tenth root of x to the third power)
see image
Step-by-step explanation:
To do this problem you need to know how to convert radicals to an expression with a fraction exponent(and back to radicals again), ALSO exponent rules for division ALSO subtracting fractions.
Square root x can be written as x^ 1/2
fifth root x can be written as x^ 1/5
When you are dividing expressions with the same base, exponent rules say to SUBTRACT the exponents.
1/2 - 1/5 change to common denominator
5/10 - 2/10
= 3/10
x^1/2 / x^1/5 =
x^ (1/2 - 1/5) =
x^ (5/10-2/10) =
x^ 3/10
Then change back to a radical. Remember "down and out" or "roots are down" and "up, up, up" or "exponents are up"
the number down below goes out (outside) the radical. And the number up top is up and exponents are up, up, up
see image.
x^3/10 =
tenth root (x^3)
see image.
he multiplication table below can be used to find equivalent ratios.
A multiplication table.
Which ratio is equivalent to the ratio 18:24?
15:20
20:15
30:36
36:30
Answer:
15:20
Step-by-step explanation:
18:24 can be written [tex]\frac{18}{24}[/tex] if I simplify this by dividing the top and bottom by 6, I get [tex]\frac{3}{4}[/tex]
I am looking for what other ration will reduce to [tex]\frac{3}{4}[/tex]
[tex]\frac{15}{20}[/tex] Divide the top and bottom by 5 and you will get [tex]\frac{3}{4}[/tex]
9. If L 1 equals 120 then what is the measure of its supplement <2=
Supplementary angles are angles whose addition sums up to 180 degrees.
Therefore, if angle 1 measures 120, then its supplement which is angle 2, must mean both add up to 180.
Hence, you have
Angle 1 + Angle 2 = 180
120 + Angle 2 = 180
Subtract 120 from both sides of the equation
Angle 2 = 180 - 120
Angle 2 = 60 degrees
By definiton, two angles are complimentary angles if they both add up to 90 degrees. Hence if angle L5 equals 50 degrees, then its compliment would be derived as 90 - 50 which equals 40. The compliment of angle L5 which is 50 degrees, equals 40 degrees.
how many pennies are in a dollar
Answer: 100
Step-by-step explanation:
$1 =100 pennies
HELP PLEASEEEEE!!!!!!
The solutions of the indices are;
1) 2^7
2) 3^-4
3) 3^4
4) 2^4
What is the power?We know that in this case, we would have to apply the laws of indices and the particular law that we are to apply in each case is dependent on the nature of the problem that have been posed. Let us recall that we are asked to ensure that we express the answer or the solution to the problem as a single power.
1) 64 * 256/128
2^6 * 2^8/2^7
2^6 + 8 - 7 = 2^7
2) 3^4/3^3 * 3^5
3^4 - (3 + 5) = 3^-4
3) 3^9/ (3^4)^1/2 * 3^3
3^9/ 3^2 * 3^3
3^9 - (2 + 3)
3^4
4) (2^3)^4 * 2^4 ÷ 32/ 2 * 64
2^12 * 2^4 ÷ 2^5/2^1 * 2^6
2^12 + 4 -5/2^1 + 6
2^16 -5/2^7
2^11/2^7
2^11 - 7
2^4
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Complete the table .....Which parts of the arithmetic sequence in the left of the table match up with the linear function on the right?
Let's expand the formula for arithmetic sequence.
[tex]\begin{gathered} a_n=a_1+d(n-1) \\ a_n=a_1+dn-d \\ a_n=dn+(a_1-d) \end{gathered}[/tex]The linear function is:
[tex]f(x)=ax+b_{}[/tex]Matching both equations, we can say:
[tex]\begin{gathered} a_n\gg\gg f(x) \\ d\gg\gg a \\ n\gg\gg x \\ a_1-d\gg\gg b \end{gathered}[/tex]Is the graph of the distance a person has driven over time an example of a continuous or discrete graph?
Let us first understand what are discrete and continuous variables.
Discrete variable:
A discrete variable is countable in a finite amount of time.
For example:
The number of coins in your pocket
The number of trees in the garden
It is not possible to have 2.5 coins or 7.3 trees
Continuous variable:
A continuous variable can take any numeric value.
For example:
The height of the tree
The room temperature
These values can be in decimal like 7.3, 0.23 etc
Now let us come to the question, the distance a person has driven can take any value
for example, it can be 50 miles or 23.4 miles or 120.5 miles
So, decimal values are possible
This means that it must be a continuous graph
The distance a person has driven over time an example of a continuous graph.