If donna didn't stop, her average speed for the final 30 miles to 2 dp is; 57.39 mph
How to Calculate Average Speed?We are given;
Distance travelled by Donna = 70 miles
Average Speed of Donna = 40 mph
Additional Distance travelled = 30 miles
Average speed for entire journey = 44 mph
We know that;
time = distance/speed
Thus
Total time = (70 + 30)/44
Total time = 100/44 h
Time 1 = 70/40 = 7/4 hr
Time 2 = 30/v
Thus;
30/v + 7/4 = 100/44
Multiply through by 44 to get;
1320/v = 100 - 77
v = 1320/23
v = 57.39 mph
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Here are some fractions.
3/10 7/20 2/5 1/4
Write these fractions in ascending order.
Answer:
1/4, 3/10, 7/20, 2/5
Step-by-step explanation:
1/4 = 25%
3/10 = 30%
7/20 = 35%
2/5 = 40%
A company decides to mix pinapple and orange soda to make a new drink.
They have 450 liters of pinapple soda, which is 42% sugar.
They mix it with 630 liters of orange soda.
The new drink is 35% sugar.
What percentage of the orange soda is sugar?
Determine the square foot of logo 2 write it out in equation form I’ll give 100 points
Answer:
45 ft²
Step-by-step explanation:
Logo 2 comprises 5 congruent squares with side length 1/2 in
Given scale: 1 in = 6 ft
⇒ 1/2 in = 3 ft
Area of a square = s² (where s is the side length)
⇒ area of one of the squares of logo 2 = (3 ft)² = 9 ft²
Therefore, the total area is:
⇒ area = 5 × 9 ft² = 45 ft²
In equation form:
A = 5(6s)²
where:
A = area (in ft²)s = side length (in inches)8) The function f(t)=12(1.8) represents the number of rabbits in a forest after t years.
a) Does the function represent exponential growth or exponential decay?
b) Graph the function on a calculator. Describe the domain and range.
c) What is the yearly percent change?
d) How many rabbits are in the forest after 8 years?
Students were asked how they traveled to school. The two-way relative frequency table
shows the results. Write answers as decimals rounded to the nearest hundredth.
Method
School
Car Bus Other TOTAL
Middle School 0.19 0.15 0.11
0.45
High School
0.33 0.13 0.09
0.55
TOTAL
0.52 0.28 0.20
1.00
What is the joint relative frequency of high school students who ride the bus?
The joint relative frequency of high school students who ride the bus is
Using the given proportions, it is found that the joint relative frequency of high school students who ride the bus is of 0.28.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The proportions relative to riding the bus in this problem are of 0.15 for middle school and 0.13 for high school, for a total of 0.28, hence, the joint relative frequency of high school students who ride the bus is of 0.28.
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please i will give brainliest if right
Answer:
s = 156.25 square meters
Step-by-step explanation:
s = 2lw + 2lh + 2wh
s = 2(5.5)(3) + 2(3)(7.25) + 2(5.5)(7.25)
s = 33 + 43.5 + 79.75
s = 156.25 square meters
Answer:
We know,
[tex] \quad [/tex][tex]{\boxed{ \rm{Surface \: Area_{ \: (rectangular \: prism)} = 2(lb + bh + hl)}}}[/tex]
where,
Height (h) = 7.25mBreadth (b) = 3mLength (l) = 5.5m[tex] \: [/tex]
[tex] {\longrightarrow { 2 ( 5.5 \times 3 + 3 \times 7.25 + 7.25 \times 5.5 ) }} [/tex]
[tex] \longrightarrow [/tex] 2 ( 16.5 + 21.75 + 39.875 )
[tex] \longrightarrow [/tex] 2 ( 78.125 )
[tex] \longrightarrow [/tex] 156.25
Thus, The Surface Area of rectangular prism is 156.25cm².
[tex] \rule{200pt}{2pt} [/tex]
Additional Information:[tex]\footnotesize{\boxed{ \begin{array}{cc} \small\underline{ \sf{\pmb{ \blue{More \: Formula}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}[/tex]
How many solutions does the following equation have? 3(2x−4) =2(3x−6)
Answer:
Infinitely many solutions
Step-by-step explanation:
Equations can either have no solutions, one solution, or infinitely many solutions.
Examples:
No solutions: 2 = 6One solution: x = 2Infinitely many solutions: 2 = 2Given: 3(2x − 4) = 2(3x − 6)
Distribute:
3(2x − 4) = 2(3x − 6)
3(2x) + 3(−4) = 2(3x) + 2(−6)
6x − 12 = 6x − 12
As both sides of the equation are identical, this equation has an infinite number of solutions.
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Factor the common factor out of each expression.
-8b+4
Answer:
Common Factor is 4.
Step-by-step explanation:
-8b + 4
Both have a 4 in it.
-8b + 4 / 4 = -2b
Let $a_1, a_2, a_3,\dots$ be an arithmetic sequence. if $a_{23} = \dfrac23$ and $a_{53} = \dfrac32$, what is $a_{35}$?
Using an arithmetic sequence, it is found that the 35th value of the sequence is given by: [tex]a_{35} = 1[/tex].
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
Considering that we have the mth term as reference, the nth term is also given as follows:
[tex]a_n = a_m + (n - m)d[/tex]
In this problem, we have that:
[tex]a_{23} = \frac{2}{3}, a_{53} = \frac{3}{2}[/tex].
Hence:
[tex]a_n = a_m + (n - m)d[/tex]
[tex]a_{53} = a_{23} + (53 - 23)d[/tex]
[tex]30d = \frac{3}{2} - \frac{2}{3}[/tex]
[tex]30d = \frac{9 - 4}{6}[/tex]
[tex]30d = \frac{5}{6}[/tex]
[tex]d = \frac{1}{36}[/tex]
Then the 35th term is:
[tex]a_{35} = a_{23} + 12d = \frac{2}{3} + 12\frac{1}{36} = \frac{2}{3} + \frac{1}{3} = 1[/tex]
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A push-cart vendor is selling sodas at the beach. partway into the day, he raises his
price per bottle by one quarter. after this price increase, the total dollar amount
collected for the day after selling n bottles at the new price is given by the following
equation:
t = 12 + 1.75n
according to this equation, how many bottles did the vendor sell today before raising the
price?
o a
8
ob.
12
c. 18
d. 21
Answer:
[tex]8[/tex].
Step-by-step explanation:
Notice that in equation for the total dollar amount collected ([tex]12+ 1.75\, n[/tex]), every additional bottle sold at the new price brings in [tex]1.75[/tex] dollars:
[tex]\begin{aligned}& 12 + 1.75\, n && \text{$n$ bottles at new price} \\ -\; & 12 + 1.75\, (n+1) && \text{$(n+1)$ bottles at new price} \\ =\; & 1.75\end{aligned}[/tex].
Therefore, the per-bottle price after the [tex]\$0.25[/tex] price increase would be [tex]\$1.75[/tex]. The per-bottle price before the price increase would be [tex]\$1.75 - \$0.25 = \$1.50[/tex].
Also notice that when [tex]n = 0[/tex], the total amount collected was [tex]t = 12 + 1.75\, n = 12[/tex]. In other words, the total amount collected was [tex]\$12[/tex] before any bottle was sold at the new price.
Thus, the vendor had collected [tex]\$12\![/tex] by selling at the initial price of [tex]\$1.50[/tex] per bottle. The number of bottles sold at that price would be:
[tex]\begin{aligned}\frac{12}{1.50} = 8\end{aligned}[/tex].
Graph the equation
x - y= -4
Answer:
y=x+4
Step-by-step explanation:
y intercept should be at positive 4 and a straight line going in the positive direction
help me
?
10
450
15
675
20
900
Answer:
Y=45x
Step-by-step explanation:
Y = f(x)
If you plot a chart, you can find that relation is just a linear relation. So y = mx + c
By putting any one case into the equation, you can find c = 0 and m = 45
Retest the equation for other cases to ensure u are correct
a right triangle has a height of 27 inches and a base of 30 inches what is the area of the triangle
Answer:
The answer is 405
Step-by-step explanation:
FIrst you would do 27 times 30 which is 810 then you would divided by 2 which in turn gives you 405
Hope this helped!
Alice and Amy decide to meet at a party. From a corner of the party hall, Amy spots Alice at the corner of the hall diagonally opposite her. If the party hall is a rectangle that measures 100 feet by 60 feet, what is the shortest distance Amy has to walk to reach Alice? Round your answer to the nearest foot.
A.
40 feet
B.
80 feet
C.
117 feet
D.
160 feet
Answer:
C) 117 Feet
Step-by-step explanation:
The question is ultimately asking for the hypotenuse of the rectangle. We can calculate that with a^2 + b^2 = c^2.
100^2+60^2=c^2
10000+3600=c^2
c^2=13600
c=116.6190379
Round --> 117
Thus the answer, C).
A guidance counselor reports that in a given semester, the probability that a student chooses art as an elective is 15 percent, the probability that a student chooses art or drama is 20 percent, and the probability that a student chooses both art and drama is 2 percent. what is the probability that a student chooses drama as an elective?
The probability that a student chooses drama as an elective is 7%.
What is the concept of probability?Probability is the study of the odds of obtaining each outcome of a random experiment. These odds are assigned the real numbers in the range between 0 and 1. Results closer to 1 are more likely to occur.
In this case, we can call:
A represents ArtD represents Drama.So, the information given was:
P(A) = 15%P(A or D) = 20%P(A and B) = 2%The formula will be:
P(A or D) = P(A) + P(D) - P(A and D)
So:
[tex]20\% = 15\% + P(D) - 2\%\\P(D) = 20\% - 15\% + 2\%\\P(D) = 7\%[/tex]
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Solve the system with
elimination.
x - y = 10
3x - 2y = 25
Answer:
Step-by-step explanation:
{x,y}={5,-5}
1. How many ounces of pure salt must be added to 11oz of
40% salt solution to produce a 75% solution? (Pure salt is 100%.)
Round your answer to the nearest hundredth of an oz.
oz.
To produce a 75% solution, it is required to add a total of 3.85 ounces of pure salt to the initial solution.
How many ounces of salt are there in the initial solution?11 oz = 100x = 40x = 11 x 40 / 100x = 4.4 ozHow many ounces of salt need to be added?4.4 oz = 40x = 75x = 75 x 4.4 / 40x = 8.258.25 - 4.4 = 3.85 ouncesLearn more about ounces in: https://brainly.com/question/26950819
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How is the graph of the parent function y=x² transformed to produce the graph of y=3(x+1)²?
O It is translated 1 unit right and compressed vertically by a factor of 3.
OIt is translated 1 unit left and compressed vertically by a factor of 3.
O It is translated 1 unit right and stretched vertically by a factor of 3.
OIt is translated 1 unit left and stretched vertically by a factor of 3.
The graph of the parent function y = x² transformed to produce the graph of y = 3(x+1)². It is translated 1 unit left and stretched vertically by a factor of 3.
How does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
The graph of the parent function y = x² transformed to produce the graph of y = 3(x+1)²
We need to find how the parent function transformed to produce the graph of y = 3(x+1)².
The parent graph is shifted 1 unit towards the left by the rule of transformation.
[tex]f(x) = f(x+1)[/tex]
By applying this rule then,
[tex]y(x) = f(x+1)^2[/tex]
Now, the parent function stretched vertically 3 times the previous graph by the rule
[tex]f(x) = 3f(x)[/tex]
Apply this rule then, we get
[tex]y(x) = 3(x+1)^2[/tex]
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find the value of n.
8 × 2^3n = 2^12
6th grade math help me
find the value of n.
8 × 2^3n = 2^12
Answer :-n = 3
Solution :-[tex]\sf\ given \:: \: 8 \times 2 ^{3n} [/tex]
[tex]\sf\rightarrow 8 \times 2 ^{3n} \: = {2}^{12} [/tex]
[tex]\sf\rightarrow {2}^{3n} = {2}^{12} \: \: (8 = {2}^{3} )[/tex]
[tex] \sf\rightarrow {2}^{3n + 3} = {2}^{12} \: \: \: ( {a}^{m} \times {a}^{n} = {a}^{m + n} )[/tex]
Equating powers since bases are same.
[tex]\sf\rightarrow 3n \: + 3 = 12[/tex]
[tex]\sf\rightarrow 3n \: + 3 - 3 = 12 - 3[/tex]
[tex]\sf\rightarrow 3n = 9[/tex]
Divide both sides by 3.
[tex]\sf\rightarrow n = 3[/tex]
Thus the value of n is 3 .
Felix’s Feed Mill sells chicken feed for $8.00 per bag. This price is no longer high enough to create a profit. Felix decides to raise the price. He is considering four different plans.
Plan A: Raise the price by $0.10 each week until the price reaches $12.00.
Plan B: Raise the price by 10 percent each week until the price reaches $12.00.
Plan C: Raise the price by the same amount each week for 8 weeks, so that in the eighth week the price is $12.00.
Plan D: Raise the price by $0.25 each week until the price reaches $12.00.
Which plan will result in the price of the feed reaching $12.00 fastest?
plan A
plan B
plan C
plan D
Answer:
B
Step-by-step explanation:
essentially the plan that increases the price the most per week reaches the goal of $12 fastest.
plan A is $0.10 per week.
plan B it is not clear, if it means 10% of the original price every week, or every week 10% of the price of the previous week. I assume the first and simplest.
that means 10% of $8 = $0.80 per week.
plan C : the same amount every week until reaching $12. we need to increase in total by $4 (from $8 to $12). to reach these $4 in 8 weeks, we need to increase the price every week by 4/8 = $0.50.
plan D : $0.25 per week.
so, the plan with the highest increase every week and therefore the fastest one reaching $12 is plan B.
Find the perimeter of the region.
41 in.
T
11 in.
T
11 in. >
I
1
I
- 41 in.-
Answer:
18 region
Step-by-step explanation:
step 1. 11+11+1=23
step 2. 23-41= -18 region
Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can
be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the
constraints on the values of x and y?
O y=5.5x; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5.
O y=5.5x; x is any real number greater than or equal to 0, and y is any real number greater than or equal to
5.5.
O y=x+5.5; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5.
O y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to
5.5.
This situation of the recipe can be represented as y=x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.
What is the equation for this situation?It is known the total amount of flour (y) is equivalent to the total amount of whole wheat flour (5.5) added to the total white flour (x). Therefore, the equation is:
y = x + 5.5
The possible values are
x = It is expected x is equalthan 0 or greater to it since the minimum amount of white flour that can be added is 0.
y = It is expected y is equal than 5.5 or greater to it since even if no
white flour is added the minimum total is 5.5.
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Answer: y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5.
1. Find the radian measure for 150 degrees.
2. Find the degree measure for π/2.
Please explain how you used the unit circle to solve these questions.
Answer:
Step-by-step explanation:
1. 150 * π/180
= 150π/180
= 5π/6
=2.62
2. π/2
π/2 * 180/π
= 90 degrees
Step-by-step explanation:
1)150° 's radian measure
[tex] \rm \implies150 \: Deg × π/180 = 2.618 \: Radians[/tex]
2)π/2 's degree measure
[tex] \rm \: \implies \: π/2 × 180/π= 180/2 = 90 \: degrees[/tex]
Basically,we need to use formulas to solve these type of sums.
can someone help me
Answer:
S=49
Step-by-step explanation:
Any triangle has an interior angle of 180.
So just add them up and set the sum equal to 180 degrees.
2s+s+33=180
3s=180-33
3s=147 . Divide both sides by 3 to isolate variable s
s=49
Given h(x) = −3 |x + 1| evaluate h (-3)
Need help this is for final’s study’s
Answer:
-6
Step-by-step explanation:
h(x) = −3 |x + 1| evaluate h (-3)
h (-3) means x = -3
Plug in:
h(x) = −3 |(-3) + 1| → h(x) = −3 |-3 + 1|
h(x) = −3 |-2| since -2 is an absolute value it becomes 2
h(x) = −3(2)
h(x) = -6
Let me know if you have anymore questions,
Good Luck studying :) YOU GOT THIS !!!
if there are 20 balloons and 5 pop how many are left
3
x + 2
3
3
12
32
12
Solve for x.
Answer:
6
explanation
[tex]since \: they \: are \: similar \\ \frac{x + 2}{32} = \frac{3}{12} \\ crossmultiplying \\ 32 \times 3 = 12(x + 2) \\ 96= 12x + 24 \\ 12x = 96 - 24 \\ 12x = 72 \\ dividing \: bothsides \: y \: 12 \\ x = \frac{72}{12} \\ x = 6[/tex]
If tan x° = 6 divided by g and sin x° = 6 divided by h, what is the value of cos x°? cos x° = h divided by g cos x° = g divided by h cos x° = gh cos x° = 6g
The value of cos x⁰ from the information given is; g/h.
What is the value of cos x⁰?According to the task content;
The value of cos x° from the information contained in the task content is required.
From conventional Trigonometry;
It follows that tan x = sin x/cos x.
On this note, it follows that;
cos x⁰ = sin x⁰/tan x⁰.
cos x⁰ = 6/h ÷ 6/g
cos x⁰ = g/h
Ultimately, the value of Cos x⁰ by evaluation is g/h.
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Answer:
cos x° = g divided by h
Step-by-step explanation:
Ms. Garcia's garden is made up of 15 corn plants and 10 squash plants. What is the ratio of the number of corn plants to the number of squash plants in Ms. Garcia's garden?
options:
A. 1:3
b.2:3
c.3:2
d. 3:1
6. Which statement is justified by the
transitive property of equality?
F. (x+y)+ z = x + (y+z)
G. If 7x = 14, then 14 = 7x
H. If -3x = y, and y = 8z, then -3x = 8z
J. x(y-z) = xy - xz
Answer:
h
Step-by-step explanation:
