Step-by-step explanation:
Since, y varies directly as x:
[tex] \therefore \: y = kx..(1) \\ (k = constant \: of \: proportionality) \\ at \: y = 21 \: and \: x = 7 \\ 21 = k \times 7 \\ k = \frac{21}{7} = 3 \\ plugging \: k = 3 \: in \: equation \: (1) \\ y = 3x..(2) \\ plugging \: \: y = - 5 \: in \: (2)\\ - 5 = 3x \\ x = \frac{ - 5}{3} \\ \: \: \: \: \: \: \huge \red{ \boxed{x = - \frac{5}{3} }}[/tex]
Answer:
X=-5/3
Step-by-step explanation:
Y=KX where k is constanty=kx21=7k divide both sides by 7to get 3then equateto get answer
10. The population of a small town was 3600 in 2005. The population increases by 4% annually.
Answer:
The growth function:
y=3600(1.04)^t
The population in 2025:
7,888
Step-by-step explanation:
I'm not sure if this is what you asked for, but I did this in my class with my teacher (algebra)
What is the nth term rule of the linear sequence below?
1
,
7
,
13
,
19
,
25
Answer:
[tex]a_{n}[/tex] = 6n - 5
Step-by-step explanation:
There is a common difference d between the consecutive terms, that is
d =7 - 1 = 13 - 7 = 19 - 13 = 25 - 19 = 6
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 1 and d = 6, thus
[tex]a_{n}[/tex] = 1 + 6(n - 1) = 1 + 6n - 6 = 6n - 5
Answer:
Step-by-step explanation:
t1 = 1 = 6 * 1 - 5
t2 =7 = 6 * 2 - 5
t3 = 13 = 6 * 3 - 5
t4 = 19 = 6*4 - 5
t5 = 25 = 6*5 - 5
-------------------------
Tn = 6n - 5
Hope it helped :)
Please help me with this question thank you
Given:
Deposit = $7500
Rate of interest = 2.75%
Time = 4 years
Compounded monthly
n = 12
To find:
The balance in the account after 4 years
Solution:
Compound interest formula:
[tex]$A=P\left(1+\frac{r}{n}\right)^{n t}[/tex]
Here P = $7500, r = 2.75%, n = 12 and t = 4.
[tex]$A=7500\left(1+\frac{2.75\%}{12}\right)^{12\times 4}[/tex]
To convert percentage into fraction, divide by 100.
[tex]$A=7500\left(1+\frac{\frac{2.75}{100} }{12}\right)^{48}[/tex]
[tex]$A=7500\left(1+\frac{0.0275 }{12}\right)^{48}[/tex]
[tex]$A=7500\left(\frac{12+0.0275 }{12}\right)^{48}[/tex]
[tex]$A=7500\left(\frac{12.0275 }{12}\right)^{48}[/tex]
[tex]$A=8371.03[/tex]
The balance in his account after 4 years is $8371.03.
Which of the following expressions are equivalent to -5.93 + (-8.62) + 5.93?
Choose 4 answers.
a. -8.62
b. −5.93 − (8.62−5.93)
c. −(5.93 + 8.62) + 5.93
d. -5.93 - 8.62 - (-5.93)
e. -5.93 − (8.62 + 5.93)
Answer:
A, B, C & D
Step-by-step explanation:
Expand and see which is is equivalent to the given expression.
In the diagram, point B is a point of tangency.Find the radius r of this diragram . THANKY YOU
Answer:
r= 18
Step-by-step explanation:
use the Pythagorean theorem to solve this
[tex]r^{2} +24^{2} =(r+12)^{2}[/tex]
[tex]r^{2}+576=r^{2} +24r+144[/tex]
-144 -144
[tex]r^{2}+432=r^{2} +24r[/tex]
-[tex]r^{2}[/tex] -[tex]r^{2}[/tex]
[tex]432=24r[/tex]
/24 /24
18=r
. My best friends and I met at the movies at
6:45pm. We were picked up at 8:15pm. How
long were we at the movies?
Answer:
1 hour and 30 minutes
Step-by-step explanation:
Answer:
the answer to this is 1 hour and 30 minutes
Step-by-step explanation:
my exlanation is one hour from 6:45 is 7:45 15 minutes until 8:00 then 15 more minute until she gets picked up. I HOPE THIS HELPS AND PLZ AND KINDLEY MARK ME BRAINLIEST HAVE A GOOD REST OF YOUR DAY =)
what is the answer pls
Given:
Surface area = 4,362 yards
Length = 36 yard
Width = 21 yard
Height = c
To find:
Volume of the rectangular prism.
Solution:
Surface area formula:
[tex]SA = 2(lw+wh+lh)[/tex]
Substitute the given values.
[tex]4362 = 2(36\times21 +21 \times c+36 \times c)[/tex]
[tex]4362 = 2(756+21 c+36 c)[/tex]
[tex]4362 = 2(756+57c)[/tex]
[tex]4362 = 1512+114c[/tex]
Subtract 1512 from both sides.
[tex]4362- 1512 = 1512+114c - 1512[/tex]
[tex]2850=114c[/tex]
Divide by 114 on both sides, we get
25 = c
Height = 25
Volume = length × breadth × height
= 36 × 21 × 25
= 18900
Volume of rectangular prism is 18900 cubic yards.
What’s the answer I don’t get this
Answer:
K(-1)=6
Step-by-step explanation:
t=-1
2 times -1 squared
-1 squared=1
2x1 = 2
2+4=6
K(-1)=6
SOMEONE PLEASE HELP MEEEEEEEEEEEEEEEEEE
Answer:
y = -(5/2)x - 1
Step-by-step explanation:
slope intercept form is y = mx + b
m is the slope
b is the y intercept
The y intercept is shown to be (0,-1), so b = -1
The equation is now y = mx -1
slope= rise/run
The rise is (4-(-1))=5
The run is (-2-0)=-2
5/-2 is the slope (m)
The equation is y = -(5/2)x - 1
Answer:
y = -5/2 x-1
Step-by-step explanation:
First we need to find the slope
m = (y2-y1)/(x2-x1)
= (-1 -4)/(0--2)
= (-5)/+2
= -5/2
We know the y intercept is -1 since that is where it crosses the y axis
We will use the slope intercept form of the equation
y= mx+b where m is the slope and b is the y intercept
y = -5/2 x-1
2n + 4n = 42
Answer: the value of n is .....
Answer:
7
Step-by-step explanation:
2n + 4n = 6n, adding like terms
6n = 42
6n/6 = 42/6
n = 7
Answer: 7
Step-by-step explanation:
4x7= 28 and 2x7=14
14+28= 42
The solid was created by connecting two congruent square pyramids to a rectangular prism.
A rectangular prism with a length of 14 inches, width of 15 inches, and height of 15 inches. 2 square pyramids with triangular sides with a height of 18 inches.
What is the surface area of this solid?
_____________ square inches
1380
1500
1920
3000
Answer:1920
Step-by-step explanation:
Answer: 1920
Step-by-step explanation:
There are 850 employees at a software company. The company’s CEO was interested in finding out if his employees prefer the new coffee brand provided in the break rooms or the old coffee brand.
A random sample of 200 employees was conducted, and 148 employees said that they prefer the new coffee brand over the old one.
The point estimate is calculated using the formula = .
Which statements are true about estimating the population proportion of employees who prefer the new coffee brand? Check all that apply.
Answer: B & E
i just took it
Step-by-step explanation:
Answer:
the answer is B and E
Step-by-step explanation:
I just took it on edg
Evaluate the expression 2x+1 , if X=4
Give the correct answer, please!!!!!!!!!!!
Answer:
9
Step-by-step explanation:
if x= 4; 2x+1
2(4) + 1
8 + 1
9
A rotation of 150° counterclockwise about the origin would be the same as a rotation of__________ clockwise about the origin.
360°
300°
30°
210°
Answer:
210
Step-by-step explanation:
360-150
think about it like going the opposite direction on a circle.
if you are on a 1 mile trail that is a circle at the starting point and you walk right to get to a marker that is half way, if you went left, the marker would be 0.5 miles the opposite direction.
Create a cylinder with a height of 8 cm and a radius of 4
cm. Make note of the volume.
Which could you do to increase the volume? Check all
that apply.
Double the height
Double the radius
Double the height but half the radius.
Double the radius but half the height.
Make the radius and height both 6 cm.
Answer: The volume is 128pi cm or 402.12 cm. To increase the volume you can double the height, double the radius, double the radius but half the height, and make the radius and height both 6 cm.
Step-by-step explanation:
To find the volume of the cylinder, use the equation [tex]\pi r^2h[/tex]. After plugging everything in, the equation is [tex]\pi (4^2)*8[/tex]. [tex]4^2[/tex]=16. 16*8=128. If you need a more accurate answer, multiply by pi to get 402.12 cm.
Doubling the height creates a volume of 256pi cm.
Doubling the radius creates a volume of 512pi cm.
Doubling the radius and halving the height creates a volume of 256pi cm.
Making both the radius and height 6 cm creates a volume of 216pi cm.
Answer:
1, 2, 4, 5
Step-by-step explanation:
your welcome.
Consider the reduction of the complex figure with a scale factor of 1
7
. What is the area of the reduced figure?
A large complex figure with 5 sides has a left side length of 28 millimeters and top side length of 42 millimeters. The area is 1225 millimeters squared. A smaller complex figure with 5 sides has a left side length of 4 millimeters and top side length of 6 millimeters.
mm2
25 cause when i put in the answer it was right
Answer:
its a on edg
Step-by-step explanation:
Consider the given triangle.
Right triangle with height labeled 8 inches, base labeled 6 inches, and third side labeled 10 inches.
How are the lengths of the sides of the triangle and the measure of its angles related?
Explain which angle would be the smallest and why.
Answer:
The angles across from the sides are related. The angle across from the side labeled 10 inches will be the largest angle and the angle across from thr side labeld 6 inches will be the smallest.
Find the volume of the cone. Leave your answer in terms of л
18 л
54л
27л
12л
Answer:
18π
Step-by-step explanation:
You have to multiply the height and the width together and then multiply by pi but since it is in terms of pi it is 18π
The volume of the cone is 18π
Option A is the correct answer.
What is a cone?It is a shape of a christmas tree where there is a base of radius r and a top point called the apex.
The volume of a cone is V = (1/3)πr²h
We have,
The formula for the volume of a cone is:
V = (1/3)πr²h
where V is the volume, r is the radius, and h is the height.
Plugging in the given values, we get:
V = (1/3) x π x 3² x 6
V = 18π
Therefore,
The volume of the cone is 18π
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How to chose a reasonable scale and interval to graph each set of data with these numbers - 70, 35, 55, 10, 43, 25, 80 and three numbers, 4,700; 2,000; 3,400; 1,650; 2,800
Answer:
For 70, 35, 55, 10, 43, 25, 80
Scale
I small square= 1 unit
For 4,700; 2,000; 3,400; 1,650; 2,800
I small square=100 unit
Step-by-step explanation:
We choose a scale such that all the points can be plotted on the graph.
For 70, 35, 55, 10, 43, 25, 80
the range of data is from 10 to 80
so if we choose I small square= 1 unit, we will be able to plot all the points on the graph.
For 4,700; 2,000; 3,400; 1,650; 2,800
the range of data is from 1600 to 4700
If we choose I small square=100 unit, we will be able to plot all the points on the graph with 1650 plotted in the middle of a small square.
what’s the lower bound of 3.115
Answer:3.1105
Step-by-step explanation:
ms.roa pays the same amount each month for internet service she is making a graph to show the amount she pays over time. Please help
Answer:
Step-by-step explanation:
Ms. Roa's monthly internet payment, being constant, would be represented by a horizontal line on a graph with time (months) on the X-axis and cost on the Y-axis. The consistency of the payment amount regardless of time represents a constant rate, demonstrated graphically.
Explanation:The subject of your question involves mathematics, specifically, the concept of the relationship between constant costs and time, which can be demonstrated using linear graphs. In Ms. Roa's case, she pays the same amount each month for internet service. This means that the cost per month is constant, so if you make a graph showing time on the X axis (in months) and cost on the Y axis, you would see a straight horizontal line, indicating that the cost does not change over time.
For example, if Ms. Roa pays $50 each month, then every point on the line will be at Y = 50 (for cost), regardless of the X value (time). The concept of a constant rate is important in understanding the relationship between different quantities, and is commonly used in Displaying Data Graphically and Interpreting the Graph.
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Please help on number 4, multiple choice
Answer:
30
Step-by-step explanation:
2 30
--- = --
? 450
same explanation as the other problem I helped you with :)
Given a=10 and B=150° in Triangle ABC, determine the values of b for which A has
A) exactly one value
B) two possible values
C) no value
Answer:
A) b > 10
B) none
C) b ≤ 10
Step-by-step explanation:
For the purpose of this answer, we assume ABC is a triangle if and only if all angles and side lengths have measures greater than 0, and the sum of angles is exactly 180°.
The fact that B = 150° means A+C = 30°. That is, 0 < A < 30°. Taking the sine of A, we have ...
0 < sin(A) < 1/2
A, B)The Law of Sines tells us ...
sin(A)/a = sin(B)/b
sin(A) = a·sin(B)/b = 10·(1/2)/b = 5/b
Substituting this into the inequality for sin(A), we get ...
0 < 5/b < 1/2
0 < 10 < b . . . . . multiply by 2b (which is > 0)
In order to form a triangle, the value of b must be greater than 10. In that case, there will always be only one value for A:
A = arcsin(5/b) . . . . b > 10
__
C)For b = 10, the "triangle" is a straight line, a disallowed condition. That is A will have no allowed value.
For b < 10, A > 30°, which forces C < 0°. This is also a disallowed condition. So we can say ...
b ≤ 10, A has no allowed value
_____
The attached diagram shows triangle ABC. Point A can be anywhere on ray BA. As segment c gets longer, angle C increases from near 0 to near 30°. At the same time, angle A decreases from near 30° to near 0°. When b=10, c=0, and the figure is not a triangle. Nor is it a triangle for b < 10.
Find the median of the following numbers. 79, 27, 24, 11, 14, 11
Answer:
19
Step-by-step explanation:
79, 27, 24, 11, 14, 11
rearrange the order
from lowest to highest
11, 11, 14, 24, 27, 79
Find the middle.
It is between 14 and 24
Take the average.
Average here = median = (14 + 24)/2 = 38/2 = 19
Final answer:
The median of the data set (79, 27, 24, 11, 14, 11) is found by first arranging the numbers in ascending order, and then taking the average of the two middle numbers, which yields a median of 19.
Explanation:
The median is the middle value of an ordered data set. To find the median, we first need to arrange the numbers in ascending order. The set of numbers given are 79, 27, 24, 11, 14, 11. Arranged in order they are 11, 11, 14, 24, 27, 79.
Since there are 6 values (an even number), we take the average of the two middle numbers. In this case, the two middle numbers are 14 and 24. Hence, we calculate the median as follows:
(14 + 24) / 2 = 38 / 2 = 19.
Therefore, the median of this data set is 19.
Help pls
I’ll put u as Brainlyest
Answer: The rule for the second question is multiple by 2
Step-by-step explanation:
Answer:
3 = 105
4 = 140
5 = 175
12 = 420
You have to multiply the 35 by what every number is on top. Like 4 for example, 35 x 4 = 140.
Angle 1 and angle 2 are what kind of angles?
Answer:
supplementary angles
Step-by-step explanation:
one angle is an obtuse angle
and another angle is an acute angel.
What is the radius of a hemisphere with a volume of 60,750π cm3?
The radius of the hemisphere is 45 cm
Explanation:
Given:
Volume of the hemisphere, V = 60750π cm³
Radius of the hemisphere, r = ?
We know:
Volume of hemisphere = [tex]\frac{2\pi r^3 }{3}[/tex]
[tex]60750\pi = \frac{2\pi r^3 }{3} \\\\r^3 = 91125\\\\r = 45[/tex]
Therefore, the radius of the hemisphere is 45 cm
The radius of the hemisphere is 45 cm
The volume of a hemisphere is given by the formula
[tex]V = \frac{2}{3} \pi r^{3}[/tex]
Where V is the volume
and r is the radius
From the question,
V = 60750π cm³
Putting this into the formula,
We get
[tex]60750\pi = \frac{2}{3}\pi r^{3}[/tex]
∴ [tex]r^{3}= \frac{60750\pi \times 3}{2\pi}[/tex]
[tex]r^{3}= 91125[/tex]
∴ [tex]r =\sqrt[3]{91125}[/tex]
r = 45 cm
Hence, the radius of the hemisphere is 45 cm
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Suppose 80% of people enjoy swimming. Suppose 70% of people enjoy running.
Suppose 55% of people enjoy doing both. What percentage of people enjoy swimming
and/or running?
Answer:
95%
Step-by-step explanation:
In this case we can apply a formula that tells us that:
# (AUB) = #A + #B - #AnB
Where A would be the ones who enjoy swimming and B would be the ones who enjoy running. AnB is the intersection of both sets, that is, those who enjoy doing both things, these values we have, if we replace them we have left:
#(AUB) = 80% + 70% - 55%
#(AUB) = 95%
Which means that 95% of people enjoy either swimming or running
The percentage of people who enjoy swimming and/or running is calculated to be 95%.
We have 80% of people who enjoy swimming, and 70% who enjoy running, with a 55% overlap of people who enjoy both.
The formula for the principle of inclusion-exclusion is:
Union = A + B - Intersection
Therefore, the percentage of people who enjoy swimming and/or running is:
Union = 80% + 70% - 55% = 95%
Hence, 95% of people enjoy at least one of the two activities.
W^2-8w=9 complete the square and round to the nearest hundredth if necessary
Answer:
w = 7, 1
Step-by-step explanation:
A perfect square is shown by a²-2ab+b²
If you substitute the question into the formula you get:
w²-(2×4×w)+4²
Simplify and you get:
w²-8w+16=9
Factor:
(w-4)²=9
Square Root both sides:
w-4=±3
w=7, w=1
If a single 9-sided die is tossed once, find the probability of rolling a number greater than 7.
The probability of rolling a number greater than 7 is
(Simplify your answer.)
Answer:
[see explanation]
Step-by-step explanation:
There are 9 numbers on the dice. (One number for each side.)
Total Number of events: 9
There are 2 numbers that are greater than seven. (8 and 9)
Preferred number of events: 2
[tex]\frac{preferred}{total} =\frac{2}{9}[/tex]
[tex]\frac{2}{9}[/tex] is already at it's lowest terms.
The probability should be 2/9.
The probability of rolling a number greater than 7 on a 9-sided die is 2/9 or approximately 22.2%.
Explanation:In the language of probability, an event is any outcome or combination of outcomes. The probability of any event is normally calculated by dividing the number of ways that the event can occur by the total number of outcomes. In this problem, a die with 9 sides is rolled once, giving a total of 9 possible outcomes (the numbers 1 to 9). The event in question is rolling a number greater than 7, which consists of two outcomes: 8 and 9. So, the probability of this event is
Number of ways the event can occur / Total number of outcomes = 2 / 9 = 0.222 (to three decimal places), or approximately 22.2%.
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