Answer:
The height is 8cm
Step-by-step explanation:
Given
[tex]L_A = 240cm^2[/tex] --- lateral area
[tex]a = 12cm[/tex] --- base lengths
Required
The height of the pyramid
The lateral area of a square pyramid is:
[tex]L_A = a\sqrt{a^2 + 4h^2[/tex]
So, we have:
[tex]240 = 12\sqrt{12^2 + 4h^2[/tex]
[tex]240 = 12\sqrt{144 + 4h^2[/tex]
Divide both sides by 12
[tex]20 = \sqrt{144 + 4h^2[/tex]
Square both sides
[tex]400 = 144 + 4h^2[/tex]
Collect like terms
[tex]4h^2 = 400 - 144[/tex]
[tex]4h^2 = 256[/tex]
Divide by 4
[tex]h^2 = 64[/tex]
Take square roots
[tex]h = 8[/tex]
Prove that if a and b are positive integers,then there exists a unique integers q and r such that a=bq+r where 0≤r<b
Step-by-step explanation:
Correct option is
C
0≤r<b
If r must satisfy0≤r<b
Proof,
..,a−3b,a−2b,a−b,a,a+b,a+2b,a+3b,..
clearly it is an arithmetic progression with common difference b and it extends infinitely in both directions.
Let r be the smallest non-negative term of this arithmetic progression.Then,there exists a non-negative integer q such that,
a−bq=r
=>a=bq+r
As,r is the smallest non-negative integer satisfying the result.Therefore, 0≤r≤b
Thus, we have
a=bq1+r1, 0≤r1≤b
the angles of a triangle is 2x,3x and 5x find the value of x
Here,
2x+3x+5x = 180 (sum of all angles of triangle are equal to 180)
or, 10x = 180
or, x = 180/10
x = 18
Therefore, the value of x is 18.
Hope this solution may help you☺
Answer:
2x + 3x + 5x = 180(sum of all the interior angles of a triangle is 180° )
10x = 180°
x=180/10
x = 18°
What is the range of g(x) = -2 [X + 3] + 2?
Answer:
A.
Step-by-step explanation:
When x = -3 g(x) = + 2 and this is the maximum value of g(x).
All other values of x give a value of g(x) < 2.
The range is (-∞, 2]
?? I got 5 minutes left, please help.
Answer:
Here we know that:
[tex]m(v) = \frac{M_0}{\sqrt{1 - \frac{V}{C} } }[/tex]
Where V is the speed, C = 3*10^8 m/s
We want to solve:
[tex]m(v) = \frac{M_0}{\sqrt{1 - \frac{V}{C} } } = 2*M_0[/tex]
We can just isolate V from the above equation, so we will get:
[tex]\frac{M_0}{\sqrt{1 - \frac{V}{C} } } = 2*M_0[/tex]
[tex]\frac{1}{\sqrt{1 - \frac{V}{C} } } = 2[/tex]
[tex]1 = 2\sqrt{1 - \frac{V}{C} }[/tex]
[tex](1/2)^2 = 1 - \frac{V}{C}[/tex]
[tex]V = (1 - (1/4))*C = (3/4)*C = (3/4)*3*10^8 m/s = (9/4)*10^8 m/s[/tex]
That is the velocity such that the effective mass is twice the rest mass.
PLEASEEEEEE HELPPPPPP IM BEGGGGINGGG SOMEONE PLEASEEEEE PLEASEEEEEEE
Answer:
x+120°+20°=180°[ sum of interior angle of triangle]
x+140°=180°
x=40°
then,
x+y= 180°[being straight line]
40°+y= 180°
y=140°
Use the digits 0 - 9 to fill in the blank.
[tex]243 \frac{1}{5} = blank[/tex]
Answer:
use 0-9 to fill in blanks
Step-by-step explanation:
State whether the data described below are discrete or continuous and explain why?
The distance between cities in a certain contry.
a. The data are discrete because the data can only take on specific values.
b. The data are discrete because the data can take on any value in an interval.
c. The data are continuous because the data can take on any value in an interval.
d. The data are continuous because the data can only take on specific values.
Answer:
c. The data are continuous because the data can take on any value in an interval.
Step-by-step explanation:
Discrete data are those which can take up only specific values. Discrete data values may include the number of children in a particular school, the number of visitors received per day. All this values are specific and cannot just take up any number one f values within an interval. Continous data on the other hand can take up any number of data values between an interval. Continous data types are usually height temperature, length(distance data). There can be infinite number of possible data within interval values.
A study is conducted to see how effective aspirin is in reducing temperature in children. A sample of 6 children suffering from influenza had their temperatures taken immediately before and 1 hour after administration of aspirin. The results are given below. We would like to conduct a paired differences t-test for this situation. The data follows:
Patient Temperature Before Temperature After Difference
1 103.7 102.6 1.1
2 103.7 102.7 1
3 100.7 98.8 1.9
4 102.7 103.5 -0.8
5 102.7 101.3 1.4
6 100.7 99.4 1.3
Mean 102.4 101.4 1
Std. Dev. 1.4 1.9 0.9
Required:
Calculate the appropriate test statistic of a matched pairs t-test for this data to see if taking aspirin will reduce a child's fever.
Answer:
Then t(s) is in the rejection region for H₀ we reject H₀ and conclude that the aspirin will reduce a child´s fever
Step-by-step explanation:
Tem.Before Tem.After diff.
103.7 102.6 1.1
103.7 102.7 1
100.7 98.8 1.9
102.7 103.5 -0.8
100.7 99.4 1.3
102.4 101.41 (Mean)
1.4 1.9 0.9 Std. Dev.
n = 6
df = 6 - 1 = 5
CI we propose to be 95 %
Then α = 5 % α = 0.05
The test is a one-tail test ( we want to know if taking aspirin will reduce a child´s fever
Hypothesis test
Null Hypothesis H₀ μd = 0
Alternative Hypothesis Hₐ μd > 0
(NOTE:) μd (average) = Temp Before - Temp. after
Therefore if μd > 0 means that there is a statistical difference between values before ( bigger ) and after or that the aspirin will reduce a child´s fever
To find t(c) from t-student table df = 5 and α = 0.05
t(c) = 2.015
To compute t(s)
t(s) = μd/ sd/√n t(s) = 0.98/ 0.9/√6
t(s) = 2.66
Comparing t(s) and t(c)
t(s) > t(c)
Then t(s) is in the rejection region for H₀ we reject H₀ and conclude that the aspirin will reduce a child´s fever
Refer to the Lincolnville School District bus data. Information provided by manufacturers of school buses suggests the mean maintenance cost per year is $4,400 per bus with a standard deviation of $1,000. Compute the mean maintenance cost for the Lincolnville buses. Does the Lincolnville data seem to be in line with that reported by the manufacturer? Specifically, what is the probability of Lincolnville’s mean annual maintenance cost, or greater, given the manufacturer’s data?
Answer:
Step-by-step explanation:
Add all of the Maintenance costs up, divide by 80. (the number of costs).
Excel formula =SUM(F2:F81) 364151.00/80 = 4551.8875 Rounded to 4552 is your answer.
If someone can pls give the answer with steps that would be greatly appreciated :)
Answer:
Slope = 3
intercept = 2
y = 3x + 2
angle y = 70
angle x = 110
Step-by-step explanation:
Which system of linear inequalities is represented by
the graph?
+
oyz_x+3 and 3x – y> 2
o ye}x+3 and 3x –y> 2
o y }x+3 and 3x + y> 2
O ya 4x+3 and 2x-y> 2
Answer:
o ye}x+3 and 3x –y> 2 system of linear inequalities is represented by the graph.
PLEASE LET ME KNOW IF ¡ AM WRONG!
The system of linear inequalities represented by the graph is
y ≥ (1/3)x + 3 and 3x - y > 2
Option A is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =≤
Greater than and equal = ≥
We have,
We see that,
When we graph,
y ≥ (1/3)x + 3 and 3x - y > 2 we get the graph shown.
y ≥ (1/3)x + 3
This inequality is positive on the y-axis.
3x - y > 2
3x > 2 + y
This inequality is positive on the x-axis.
Thus,
The system of linear inequalities represented by the graph is
y ≥ (1/3)x + 3 and 3x - y > 2
Learn more about inequalities here:
https://brainly.com/question/20383699
#SPJ7
ANSWER ALL QUESTIONS
1. In a class of 28 pupils, 13 have pencils, 9 have erasers and 9 have neither pencils nor erasers. How
many pupils have both pencils and erasers?
2. A universal set, U consists of prime numbers with P and Q as subsets of U. If P and Q are given by
P = {n: 3(n + 1) = 2(n + 10)}, and Q = {n: 7<n<31}, list the elements of P n Q.
1. 3
29-9=19
13+9=22
22-19=3
I don't know number 2, sorry.
The rectangle was rotated 360° around its center, point
C. Vertex D traces the path of a circle and lands back
Which best explains why the rotation represents an
isometric transformation?
upon itself.
y
O The angle at point D remained a right angle.
O The rectangle did not change shape or size.
O Point C remained the center of the rectangle.
5
D
4
Point C did not remain the center of the rectangle.
3
2+
1
с
+
1
43 -2 -11
2
3
4.
-2+
-3+
Answer:
O The rectangle did not change shape or size.
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Isometric transformation is a transformation that preserves the shape and size of the figure. Types of isometric transformations are reflection, translation and rotation.
The rectangle represents an isometric transformation because the rectangle did not change shape or size.
don’t understand this help please
Step-by-step explanation:
Since he sold $70,834 worth of cars, he earned an extra 5% commission on the sale. That means he got
0.05×($70,834) = $3,541.70
Therefore, his salary for the month m is
m = $2250 + 0.05s = $2,250 + $3,541.70 = $5,791.70
At a school camp there is enough foot for 150 students for 5 days.
Q: How long would the food last if there were only 100 students?
Answer:
Step-by-step explanation:
you need to find how much food is used for 1 person then times that answer by 100 to find how much food is needed
I don't understand plz help
9514 1404 393
Answer:
x = 2
Step-by-step explanation:
Triangles QST and QSR are congruent, so angle QST is congruent to angle QSR.
(3x +24)° = 30°
3x = 6 . . . . . . . . . divide by °, subtract 24
x = 2 . . . . . . . . . . divide by 3
__
Additional comment
What matters here is the relationship between the two marked acute angles. The fact that point Q is equidistant from the sides of angle TSR tells you that QS is an angle bisector and the two angles have equal measures. (The definition of an angle bisector is that it is equidistant from the sides of the angle.)
Recognition that the two triangles are congruent is another way to see that the marked acute angles have the same measure. The triangle congruence can be claimed on the basis of the HL theorem, since both are right triangles, have the same hypotenuse (QS), and have legs (QT, QR) with the same measure.
Which graph has a slope of 4/5
Answer: whichever graph that goes up 4 and over 5
Step-by-step explanation:
rise over run, 4 up, 5 right
to find it just look at two points on the line and count how many up and how many horizontal units there are between them :)
The Utica Boilermaker is a 15-kilometer road race. Sara is signed up
to nin this race and has done the following training runs:
I.
10 miles
II.
44,880 feet
III. 15,560 yards
Which run(s) are at least 15 kilometers?
Answer:
10 miles
Step-by-step explanation:
10 miles= 16093.44km
44880ft=13.679424km
15560yards= 14.228064
ASAP PLEASE!!The table and the relative frequency histogram show the distribution of the number of tails and three coins are tossed. Find the probability P(T=1). write your answer as a fraction.
Explanation:
P(T = 1) is the notation that means "The probability of getting exactly one tail". The table shows 3/8 in the bottom row, under the "1" in the top row. So that's why P(T = 1) = 3/8
Or it might make more sense to say P(one tail) = 3/8 so we don't have too many equal signs going on.
help me please it’s timed !!!
While
AB is A. 5Welcome :)a bag contains 5white and 3red identical balls.if the balls are drawn at random after the other without replacement. what is the probability that the first red ball is picked at fifth draw
Answer:
2/7
Step-by-step explanation:
The playground director has a total of
24 basketballs and footballs. He has
6 more footballs than basketballs, How
many of each does he have?
Answer:
9 basketballs
15 footballs
Step-by-step explanation:
The number of basketballs will be y.
The number of basketballs will be y + 6.
y + y + 6 = 24
2y + 6 = 24
2y + 6 - 6 = 24 - 6
2y = 18
2y ÷ 2 = 18 ÷ 2
y = 9
y + 6
9 + 6 = 15
What equation can you write to solve for x?
Answer:
(3x) ° + (x+ 10)° = 90°
Step-by-step explanation:
(3x) ° + (x+ 10)° = 90°
3x + x + 10 = 90
4x = 90 - 10
4x = 80
x = 20
(3x) ° = 3 x 20 = 60°
(x + 10)° = 20 + 10 = 30°
Answer: you can either do 3x°(x+10)° or (x+10)°+3x°
the choice is yours. Hope this helps
what is the solution for 3(x+3)=12
Answer: 3×4=12
Step-by-step explanation:
Brackets: X=1 , so 1+3=4 and 3+4=12
Carson is going to see a movie and is taking his 2 kids. Each movie ticket costs
$14 and there are an assortment of snacks available to purchase for $3.50
each. How much total money would Carson have to pay for his family if he
were to buy 2 snacks for everybody to share? How much would Carson have
to pay if he bought x Snacks for everybody to share?
Total cost with 2 snacks:
Total cost with x sn
acks:
49 dollars
Step-by-step explanation:
14 times 3 is 42 and 3.50 times 2 is 7, so 42 plus 7 is 49.
Total cost with 2 snacks = $35
Total cost with x snacks = 28+3.50x
Given :
Carson is going to see a movie and is taking his 2 kids. Movie ticket costs $14 and snacks cost $3.50.
Explanation :
Carson buys 2 snacks . we need to find the total cost that Carson have to pay where he buy 2 snacks.
Total cost = cost of ticket (2 kids) + cost of 2 snacks
[tex]Total \; cost = 14(2) + 2(3.50)=35[/tex]
Total cost with 2 snacks = $35
Total cost with x snacks = cost of ticket (2 kids) + cost of x snacks
[tex]Total \; cost = 14(2) + 3.50(x)\\Total \; cost = 28+3.50x[/tex]
Total cost with x snacks = 28+3.50x
Learn more : brainly.com/question/17565961
Find the value of x.
Plz help :/
Answer:
10
Step-by-step explanat
ion:
If someone can pls give the answer with steps that would be greatly appreciated :)
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]
The measures of [tex]x[/tex] and [tex]y[/tex].
[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\: 210°\:and\:\:y\:=\: -30°}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
An exterior angle of a triangle is equal to sum of two opposite interior angles.
And so we have,
[tex] 40° = 70° + y[/tex]
[tex]➪ \: y= 40° - 70°[/tex]
[tex]➪ \: y = - 30°[/tex]
Also,
[tex]\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}[/tex]
[tex]y[/tex] + [tex]x[/tex] = [tex]180°[/tex]
[tex]➪ \: -30° + x= 180°[/tex]
[tex]➪ \:x = 180° + 30°[/tex]
[tex]➪ \:x = 210°[/tex]
[tex]\sf\purple{Therefore,\:the\:measures \:of\:the\:unknown\:angles\:are\:"x=210°"\:and\:"y=-30°.}[/tex]
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]
Noel and Casey both start at the same place. Noel walks due south and Casey walks due east. After some time has passed, Noel is 6 miles south and Casey is 8 miles east. At this time, Noel is walking at a rate of 2 mph and Casey is walking at a rate of 1 mph. How fast is the distance between them increasing at this time
Answer:
2.04 miles per hour
Step-by-step explanation:
Given
Noel
[tex]n_1 =6miles[/tex]
[tex]r_1 = 2mph[/tex]
Casey
[tex]c_1 = 8miles[/tex]
[tex]r_2 =1mph[/tex]
Required
The rate at which the distance increases
Their movement forms a right triangle and the distance between them is the hypotenuse.
At [tex]n_1 =6miles[/tex] and [tex]c_1 = 8miles[/tex]
The distance between them is:
[tex]d_1 = \sqrt{n_1^2 + c_1^2}[/tex]
[tex]d_1 = \sqrt{6^2 + 8^2}[/tex]
[tex]d_1 = \sqrt{100}[/tex]
[tex]d_1 = 10miles[/tex]
After 1 hour, their new position is:
New = Old + Rate * Time
[tex]n_2 = n_1 + r_1 * 1[/tex]
[tex]n_2 = 6 + 2 * 1 = 8[/tex]
And:
[tex]c_2 = c_1 + r_2 * 1[/tex]
[tex]c_2 = 8 + 1 * 1 = 9[/tex]
So, the distance between them is now:
[tex]d_2 = \sqrt{n_2^2 + c_2^2}[/tex]
[tex]d_2 = \sqrt{8^2 + 9^2}[/tex]
[tex]d_2 = \sqrt{145}[/tex]
[tex]d_2 = 12.04[/tex]
The rate of change is:
[tex]\triangle d = d_2 -d_1[/tex]
[tex]\triangle d = 12.04 -10[/tex]
[tex]\triangle d = 2.04[/tex]
Suppose that y varies inversely with x. Write a function that models the inverse function x=7 when y=3
9514 1404 393
Answer:
y = 21/x
Step-by-step explanation:
The inverse variation relation means ...
y = k/x
For the given values, we can determine the constant k:
3 = k/7
3×7 = k = 21
Then the function is ...
y = 21/x
A ream of a certain brand of paper weighs about 4.533 pounds. A ream contains 500 sheets of paper. How much does a sheet of paper weigh?
Step-by-step explanation:
As a ream or
500
sheets of paper weigh
4.818
pounds
One sheet of paper weighs
4.818
500
=
0.009636
pounds.
It is apparent that pound is too big a unit for a sheet of paper.
As each pound has
16
ounces, one can say
one sheet of paper weighs
0.009636
×
16
=
0.154176
ounces.
If ounce is too big, as we have
1
pound equal to
28.34952
grams
one sheet of paper weighs
0.154176
×
28.34952
≈
4.371
grams
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