Answer:
About 6400
Step-by-step explanation:
Round all values: 316 --> 320, 4.03 --> 4, 0.198 --> 0.2
Expression: 320*4/0.2
Multiply: 320*4 = 1280, 1280/0.2
Divide: 2180/0.2 = 6400
316 times 4.03 equals 1273.48 then divide the product by 0.198 and you should get 6431.71717 and could round to 6432. sorry if this is wrong but have a wonderful day
A text message plan costs $3 per month plus $0.37 per text. Find the monthly cost for x text messages
Answer:
C=3+.37x
Step-by-step explanation:
C=cost/month
x=number of messages sent
Answer:
3 + 0.37x
Step-by-step explanation:
A text message plan costs $3 per month plus $0.37 per text.
Cost of x message with the given rate = (0.37x)
Total monthly cost = ( 3 + 0.37x )
Therefore, monthly cost of x messages will be represented by 3 + 0.37x
Which function has a period equal to half the period of the function in y = -3sin(2/3x - 2π) + 2?
a. y = 3cos(2/3x - π) + 2
b.y = -3/2cos(2/3x - 2π) + 2
c.y = -3cos(2/3x - 2π) + 2
d.y = 3cos(4/3x - 2π) + 2
Answer:
D. [tex]y=3\cos(\frac{4}{3}x-2\pi)+2[/tex]
Step-by-step explanation:
The given function is:
[tex]y=-3\sin(\frac{2}{3}x-2\pi)+2[/tex]
This function is of the form:
[tex]y=A\sin(Bx-C)+D[/tex], where [tex]B=\frac{2}{3}[/tex]
The period is given by:
[tex]T=\frac{2\pi}{B}[/tex]
[tex]T=\frac{2\pi}{\frac{2}{3}}=3\pi[/tex]
Half of this period is [tex]\frac{3\pi}{2}[/tex].
The function that has a period of [tex]\frac{3\pi}{2}[/tex] is
[tex]y=3\cos(\frac{4}{3}x-2\pi)+2[/tex]
Answer:
d.y = 3cos(4/3x - 2π) + 2
Step-by-step explanation:
The quantity q varies inversely with the square of m and directly with the product of rand x. When q is 2.5, m is 4 and the
product of r and x is 8. What is the constant of variation?
Answer:
The constant of variation is
[tex]k= 5[/tex]
Step-by-step explanation:
First we must write the relationship as an equality.
If q varies inversely with the square of m, this means that when m ^ 2 increases then q decreases.
If q varies directly with the product of r and x this means that when r * x increases q increases.
Then the relationship is:
[tex]q = k\frac{rx}{m^2}[/tex]
Where k is the constant of proportionality
Then if:
[tex]q=2.5\\\\m=4\\\\r*x=8[/tex]
[tex]2.5 = k\frac{8}{4^2}[/tex]
We solve for k
[tex]2.5 = k\frac{8}{16}[/tex]
[tex]2.5 = k\frac{1}{2}[/tex]
[tex]k= 5[/tex]
Answer:
5
Step-by-step explanation:
C on edge
Design a new cereal box that will hold the same amount of cereal but reduce manufacturing costs. Prove that your new design holds the same amount but can be manufactured more cheaply.
*My box costs $11.6
So I have a rectangular prism thats
8 in-length
1 in-width
12 in-height
the volume is 96 in. and the surface area is 232
*If you could show your work that would be great. *
Final Answer:
The proposed new cereal box design has dimensions of 6 inches in length, 2 inches in width, and 8 inches in height. This design maintains the original cereal volume of 96 cubic inches while reducing the surface area to 104 square inches.
Explanation:
The formula for the surface area [tex](\(A\))[/tex] of a rectangular prism is given by:
[tex]\[ A = 2lw + 2lh + 2wh \][/tex]
For the original box with dimensions 8 inches in length [tex](\(l\)),[/tex] 1 inch in width [tex](\(w\)),[/tex] and 12 inches in height [tex](\(h\))[/tex]:
[tex]\[ A_{\text{original}} = 2(8 \times 1) + 2(8 \times 12) + 2(1 \times 12) = 232 \][/tex]
For the proposed new design with dimensions 6 inches in length, 2 inches in width, and 8 inches in height:
[tex]\[ A_{\text{new}} = 2(6 \times 2) + 2(6 \times 8) + 2(2 \times 8) = 104 \][/tex]
Comparing the surface areas, the new design significantly reduces it from 232 square inches to 104 square inches. This reduction in surface area indicates that the proposed design will require less material for manufacturing.
By maintaining the original cereal volume of 96 cubic inches while decreasing the surface area, the proposed cereal box design is more cost-effective to manufacture. The optimization of dimensions ensures that the same cereal quantity can be accommodated with a reduction in manufacturing costs.
The population of a town increased from 5600 to 6300 people. What was the percent of increase
well, the difference is just 6300 - 5600 = 700.
if we take 5600 to be the 100%, what is 700 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 5600&100\\ 700&x \end{array}\implies \cfrac{5600}{700}=\cfrac{100}{x}\implies 8=\cfrac{100}{x} \\\\\\ 8x=100\implies x=\cfrac{100}{8}\implies x=\cfrac{25}{2}\implies x=12.5[/tex]
Answer:
12.5
Step-by-step explanation:
A function is defined as follows: For which x-values is y = -9? Select all that apply.
-4.5
-3
3
9
Answer:
3
Step-by-step explanation:
y = -9 when x = 3
When x = -4.5, the first definition of the function will be used since -4.5 is less than -3. In this region, y = -x implying that when x = -4.5, y= 4.5.
When x = 3, the last definition of the function will be used since 3 is greater than -2. In this region, y = -x^2 implying that when x = 3, y= -9.
Answer:
3
Step-by-step explanation:
In the given right triangle, find the missing length.
12 m
39 m
28 m
14 m
Answer:
a = 12
Step-by-step explanation:
pythag. theorem.
a^2 + b^2 = c^2
a = ?
b = 1225
c = 1369
solve
uwu
Help, hurry up please
For this case we must find an expression equivalent to:
[tex]\frac {\sqrt [7] {x ^ 2}} {\sqrt [5] {y ^ 3}}[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So, rewriting the expression we have:
[tex]\frac {x ^ {\frac {2} {7}}} {y ^ {\frac {3} {5}}} =[/tex]
By definition of power properties we have:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
So:
[tex]x ^ {\frac {2} {7}} * y ^ {- \frac {3} {5}}[/tex]
Answer:
Option A
Answer:
The correct answer is second option
(√x²/⁷)(√y⁵/³)
Step-by-step explanation:
Points to remember
Identities
Xᵃ * Xᵇ = x⁽ᵃ⁺ᵇ⁾
Xᵃ/Xᵇ = X⁽ᵃ⁻ᵇ⁾
1/Xᵃ = X⁻ᵃ
X¹/ᵃ = 1/Xᵃ
To find the correct option
From the figure we can see that,
7√x²/5√y³
Using identities we can write,
7√x²/5√y³ = (√x²/⁷)/(√y³/⁵
= (√x²/⁷) * (√y⁵/³)
Therefore the correct answer is second option
(√x²/⁷)(√y⁵/³)
What is the area (in square units) of the region under the curve of the function f(x)=x+3, on the interval from x=1 to x=3 ?
Answer:
10 square units
Step-by-step explanation:
We want to find the area under the curve [tex]f(x)=x+3[/tex] from x=1 to x=3.
We use definite integrals to find this area.
[tex]\int\limits^3_1 {x+3} \, dx[/tex]
We integrate to obtain:
[tex]\frac{x^2}{2}+3x|_1^3[/tex]
We evaluate the limits to get:
[tex]\frac{3^2}{2}+3(3)-(\frac{1^2}{2}+3(1))[/tex]
[tex]4.5+9-0.5-3=10[/tex]
Therefore the area under the curve from x=1 to x=3 is 10 square unit.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Polygon ABCD, shown in the figure, is dilated by a scale factor of 8 with the origin as the center of dilation, resulting in the image A′B′C′D′.
The slope of is
.
Answer:
2 the answer is 2/1 but just write 2
Step-by-step explanation:
Dilation of a polygon by a factor of 8 enlarges the polygon without changing the slope of the line. Therefore, the slope of AB and A'B' are the same. Further information is needed to provide a numerical value.
Explanation:Since the polygon is dilated by a scale factor of 8, the new image A′B′C′D′ is an enlargement of the original polygon ABCD by a factor of 8. The slope of a line in a dilation remains the same, even if the length of the line is changed. Essentially, the steepness of a line isn't affected by dilations. Therefore, the slope of AB and A'B' are same. Since the slope of AB is not given in the question, it's necessary to have that information to answer your question completely.
Learn more about Dilation of Polygons here:https://brainly.com/question/30429735
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amie has 9 cats. each cat eats 1/3 can of food each day. how many cans of food are used each day?
Answer:
3 Cans.
Step-by-step explanation:
Each cat can take one portion. so
9 ÷ 3 = 3
3 cans a day
Vic sells ice creams.
The table shows the midday temperature and her sales for five days.
Mon Tues Wed Thur Fri
Temperature (°C) 24 30 28 19 17
Sales (£)
225 260 230 180 150
Work out Vic's total profit for the five days.
This table shows Vic's costs.
Ingredients 12% of sales
Fuel £9 per day
Answer:
Hi the answer is 874.6
Step-by-step explanation:
1. Add all numbers to equal 1,045
2. Times the number by 12% so .12
to equal 125.4
3 subtract 125.4 by 1045 to equal 919.6
4. Times 9 by 5(the number of days) to equal 45
5. Finally subtract 45 by 919.6 to equal 874.6
Hope this helped. Have a great day!
The total profit of Vic for the five days of sales given the cost of ingredients and fuel is £874.60.
What is the total profit?Total profit is the total revenue less total cost.
Total revenue = 225 + 260 + 230 + 180 + 150 = £1045
Cost of ingredients = 12% x 1045 = $125.40
Total fuel = £9 x 5 = £45
Profit = £1045 - £45 - £125,40 = £874.60
To learn more about profit, please check: https://brainly.com/question/26181966
How is eight thousand,seventy-six written in standard form
8,076 ....................
Answer:
8076
Step-by-step explanation:
You need a 4-digit number. The leftmost digit is the thousands digit (T). The next digit to the right is the hundreds digit (H). The third digit from the left is the tens digit (E), and the rightmost digit is the ones digit (O).
Using T, H, E, and O, as shown above, the number will have the form:
THEO
Now you replace each letter with the correct digit.
"eight thousand, seventy-six" has no hundreds, so let's include hundreds:
"eight thousand (T = 8), zero hundreds (H = 0), and seventy (E= 7)-six (O = 6)"
8076
The important thing is to remember to include a 0 as the digit for the hundreds place.
Please answer right away
Answer:
6.13
Step-by-step explanation:
Using Sine Law we know that
[tex]\dfrac{a}{SinA}=\dfrac{b}{SinB}=\dfrac{c}{SinC}[/tex]
Using your figure let's assign sides and angles:
A=? B = 60° C = 70°
a = 5 b = ? c = x
If we put that into our formula:
[tex]\dfrac{5}{Sin?}=\dfrac{?}{Sin60}=\dfrac{x}{Sin70}[/tex]
Notice that we have too many unknowns. We need to complete at least one ratio to do this, so how do we do this?
Notice we have 2 angles given, so we solve for the third angle. The sum of all angles in any triangle is always 180°
∠A + ∠B + ∠C= 180°
∠A + 60° + 70° = 180°
∠A + 130° = 180°
∠A = 180° - 130°
∠A = 50°
Now we can use this to solve for x.
[tex]\dfrac{5}{Sin50}=\dfrac{x}{Sin70}\\\\\dfrac{(5)(Sin70)}{Sin50} = x\\\\\dfrac{4.6985}{0.7660}=x\\\\6.1338 =x[/tex]
So the closest answer would be 6.13
Answer:
The correct answer option is 6.13.
Step-by-step explanation:
We are given a scalene triangle which has no equal side and we are to find the unknown side length x.
Since the total measure of angles of a triangle is 180°, so we can find the measure of the unknown angle.
180° - 70° + 60° = 50°
Now we can use the sine formula to find the value of x.
[tex]\frac{x}{sin70} =\frac{5}{sin50}[/tex]
[tex]x=\frac{5}{sin50} \times sin70[/tex]
[tex]x=6.13[/tex]
Find f-1 for the function f(x)=4x+2 MATH 3 question. 10 points. HELP NEEDED.
Answer:
f^-1(x) = (x - 2)/4 ⇒ 1st answer
Step-by-step explanation:
* Lets revise how to find the inverse function
- At first write the function as y = f(x)
- Then switch x and y
- Then solve for y
- The domain of f(x) will be the range of f^-1(x)
- The range of f(x) will be the domain of f^-1(x)
* Now lets solve the problem
∵ f(x) = 4x + 2
∴ y = 4x + 2 ⇒ switch x and y
∴ x = 4y + 2 ⇒ subtract 2 from both sides
∴ x - 2 = 4y ⇒ ÷ 4 both sides
∴ (x - 2)/4 = y
∴ f^-1(x) = (x - 2)/4
* f^-1(x) = (x - 2)/4
If x/-9=-18 what does x equal
Answer: X is equal to 162
Step-by-step explanation:
You multiply the result of -18 by the -9 because these two would equal the number for X.
Negative times a negative is a positive.
Answer: 162
StepsEquation: x / -9 = -18
Multiply both sides by -9
x / -9( -9 ) = ( -18 )( -9 )
Simplify (Multiply -18 by -9)
x = 162
Identify the recursive formula for the following sequence:
1/2, 1 1/2, 3 1/2, 7 1/2...
Answer:
C
Step-by-step explanation:
The problem is where does n start?
a1 = 1/2
a2 = 2*(a1) + 1/2
a2 = 2*(1/2) + 1/2
a2 = 1 + 1/2
a2 = 1 1/2
=========
a3 = 2*a2 + 1/2
a3 = 2*(1 1/2) + 1/2
a3 = 3 + 1/2
a3 = 3 1/2
==============
a4 = 2(3 1/2) + 1/2
a4 = 7 + 1/2
a4 = 7 1/2
==============
an = 2*a_(n-1) + 1/2
The answer is C
Answer:
C on edge my loves
Step-by-step explanation:
Find the slope of the line.
Answer:
-1/4
Step-by-step explanation:
Answer:y=mx+b
Step-by-step explanation:
y would be the slope of the beginning of equation
What is the value of the interquartile range of the data below?
6
12
14
24
Answer:
14
Step-by-step explanation:
The interquartile range is the value of quartile 3 minus quartile 1.
The "box" part of this diagram has 3 lines, the left most, the middle, and the rightmost.
The leftmost line is Quartile 1. The right most is Quartile 3.
Hence
interquartile range = quartile 3 - quartile 1
Looking at the box plot, we can see that each small line in the number line is 2 units.
The leftmost line (quartile 1 ) is at 1 unit left of 30, so that is 30 -2 = 28
The rightmost line (quartile 3) is at 1 unit right of 40, so that is 40 + 2 = 42
Hence,
Interquartile range = 42 - 28 = 14
Answer:
c: 14
Step-by-step explanation:
I see everyone saying it is B or D, but ITS C! The graph is counting by 2, so there fore it is 42-28= 14. :)
A fish is swimming at 500 KM/hour and suddenly as shark appears behind, for 5 seconds the fish is swimming in the same direction but increases its speed to 2500 Km/H What is its average acceleration?
Answer:
[tex]a =111.1\ m/s^2[/tex]
Step-by-step explanation:
The formula to calculate the average acceleration is:
[tex]a =\frac{s_2-s_1}{t_2-t_1}[/tex]
Where s is the speed of the object and t is the time it takes the object to change its speed [tex]s_1[/tex] to the speed [tex]s_2[/tex]
In this case we have that:
[tex]t_2-t_1 = 5\ sec[/tex]
[tex]s_1 = 500\ km/h = 500*\frac{1\ h}{3600\ s}*\frac{1000\ m}{1\ km}=138.89\ m/s[/tex]
[tex]s_2= 2500\ km/h = 2500*\frac{1\ h}{3600\ s}*\frac{1000\ m}{1\ km}=694.44\ m/s[/tex]
[tex]a =\frac{694.44-138.89}{5}\ m/s^2[/tex]
[tex]a =111.1\ m/s^2[/tex]
The figure is made up of a cylinder and a spear which has been cut in half. The radius of each half sphere is 5 mm. What is the volume of the composite figure? Use 3.14. Round to the nearest hundredth
Answer:
The volume of the cylinder should be:
V = Bh = πr²h = 3.14 · 5² · 10 = 785 (mm³)
The volume of the sphere should be:
V = 4/3 · πr³ = 4/3 · 3.14 · 5² ≈ 523.33 (mm³)
=> The total volume of the composite figure is:
V = 785 + 523.33 = 1,308.33 (mm³)
Answer:
V = 785 + 523.33 = 1,308.33 (mm³)
Step-by-step explanation:
10.
The class was asked to find the area for a circle with a diameter of 12cm. Brandy solved the
problem showing all her work. Find and explain the error Brandy made. Then solve for the
correct answer
A= her?
A= 3.14 x 122
A = 452.2cm
Answer:
383.08
Step-by-step explanation:
Multiply 3 times 122 which is 366
Then multiply .14 times 122 which is 17.08
Then add.
Final answer:
Brandy's mistake was not converting the diameter to the radius before applying the area formula A = πr². The correct area of a circle with a diameter of 12 cm is 113.04 cm², but it should be reported as 110 cm² to maintain two significant figures.
Explanation:
The error in Brandy's solution for finding the area of a circle with a diameter of 12 cm lies in not first converting the diameter into the radius. The formula for the area of a circle is A = πr², where r is the radius and π (pi) is approximately 3.14. Since the radius is half of the diameter, for a diameter of 12 cm, the radius is 6 cm. Thus, the correct calculation is A = 3.14 × 6².
Correct solution:
A = 3.14 × 6 cm²
A = 3.14 × 36 cm²
A = 113.04 cm²
As for the significance of figures, since the radius has two significant figures (6 cm), the calculated area should also be limited to two significant figures, rounding to 110 cm².
a regular pentagon had a perimeter of 25m and an area of 43.75m2 find the perimeter of a similar pentagon whth an area of 175m2
Answer:
50 cm
Step-by-step explanation:
Since the figures are similar then
linear ratios = a : b
area ratios = a² : b²
Here the ratio of areas = 43.75 : 175 = 1 : 4, thus
linear ratios = 1 : 2
The larger pentagon has a perimeter = 2 × 25 = 50 cm
Identify the restrictions on the variable
Answer:
x ≠ -4
Step-by-step explanation:
Division by zero is not defined, so x cannot = -4.
Whoever answers this will get 75 point! How do I find the MEAN, give the process, of the data set? City A: {3, 4, 6, 4, 3, 1, 4} City B: {6, 7, 2, 4, 5, 5, 3}
Answer:
Step-by-step explanation:
Mean is just another word for average. To find the average, add up all the values then divide by the number of values.
There are 7 values in the first data set. The average is:
(3 + 4 + 6 + 4 + 3 + 1 + 4) / 7 = 25/7 ≈ 3.57
There are 7 values in the second data set. The average is:
(6 + 7 + 2 + 4 + 5 + 5 + 3) / 7 = 32/7 ≈ 4.57
Which word best describes the degree of overlap between the two data sets?
none
low
moderate
high
The best word that describes the degree of overlap between the two data sets is: low.
What is Degree of Overlap?The degree of overlap between two sets of data can be described as the extent to which two data sets vary in terms of their centers.
In the diagram given, the two dot plots overlap between 30 and 35. The difference is minimal.
Therefore, the best word that describes the degree of overlap between the two data sets is: low.
Learn more about degree of overlap on:
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Answer: The word that best describes the degree is B Low
Explanation: I took the test and it was right.
Hope ya'll have a good day :)
what Is the midpoint between A (3,4) and B (-3,-6)
Answer:
Step-by-step explanation:
X: (x1 + x2)/2 = (3 - 3)/2 = 0/2 = 0
y: (y1 + y1)/2 = (4 - 6)/2 = -2/2 = - 1
Midpoint (0,-1)
ANSWER
[tex](0, - 1)[/tex]
EXPLANATION
The midpoint formula is given by:
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
To find the midpoint of the segment joining A (3,4) and B (-3,-6), we substitute the points into the formula:
[tex](\frac{3+ - 3}{2},\frac{4+ - 6}{2})[/tex]
We simplify to obtain;
[tex](\frac{0}{2},\frac{ - 2}{2})[/tex]
This gives us;
[tex](0, - 1)[/tex]
The midpoint of line segment AB is (0,-1)
A box contains 100 colored chips; some are yellow and some are green. John chooses a chip at random, records the color, and places it back in the bag. John has recorded 57 yellow chips and 19 green chips. Using these results, what is the predicted number of green chips in the box?
25
43
76
81
Answer:
25
Step-by-step explanation:
A box contains 100 colored chips
Some are yellow and,
Some are green.
John has recorded 57 yellow chips and 19 green chips.
The ratio of yellow chips to green chips is 57:19 simplified becomes; 3:1
The number of green chis is [tex]\frac{1}{3 + 1}[/tex] × 100 = [tex]\frac{1}{4}[/tex] × 100 = 25
In school 40% of the students play tennis, 24% of the students play baseball, and 58% of the students playing neither tennis or baseball, if you pick a student at random what is the probability that the student plays both tennis and baseball
Answer: The required probability that the random student selected plays both tennis and basketball is 22%.
Step-by-step explanation: Given that in a school, 40% of the students play tennis, 24% of the students play baseball, and 58% of the students playing neither tennis or baseball.
We are to find the probability that a random student picked plays both tennis and basketball.
Let the total number of students in the school be 100. Also, let T and B represents the set of students who play tennis and basketball respectively.
Then, according to the given information, we have
[tex]n(T)=40,~~~n(B)=24.[/tex]
The number of students who play either tennis or basketball will be represented by T ∪ B.
And so, we have
[tex]n(T\cup B)=100-58=42.[/tex]
We know that the number of students who play both tennis and basketball is denoted by T ∩ B.
From set theory, we get
[tex]n(T\cup B)=n(T)+n(B)-n(T\cap B)\\\\\Rightarrow n(T\cap B)=n(T)+n(B)-n(T\cup B)\\\\\Rightarrow n(T\cap B)=40+24-42\\\\\Rightarrow n(T\cap B)=22.[/tex]
Thus, the required probability that the random student selected plays both tennis and basketball is 22%.
17. The distance between (2, 1) and (n, 4) is 5 units. Find all possible values of n.
Answer:
6=n and -2=n
Step-by-step explanation:
The distance between two points is found by
d = sqrt(( x2-x1)^2 + (y2-y1)^2)
5 = sqrt(( n-2)^2 + (4-1)^2)
5 = sqrt(( n-2)^2 + (3)^2)
Square each side
5^2 = sqrt(( n-2)^2 + (3)^2)^2
25 = ( n-2)^2 + (3)^2
25 = (n-2)^2 +9
Subtract 9 from each side
25-9 = (n-2)^2 +9-9
16 = (n-2)^2
Take the square root of each side
sqrt(16) = sqrt( (n-2)^2)
±4 = n-2
Add 2 to each side
2±4 = n-2+2
2 ±4 = n
2+4 =n and 2-4 =n
6=n and -2=n