Answer:
-3
Step-by-step explanation:
because it has a negitve sign
Answer:
-3
look at this number line
________________________________
-4 -3 -2 -1 0 1 2 3 4
The numbers on the left side of the 0 are negative since they have a value below zero. This can be represented as a - (negative) sign
Step-by-step explanation:
Keep in mine this number line can continue forever meaning every possible number on the left side of the 0 is negative.
Mai has a dome paperweight that she can use as a magnifier. The paperweight is
shaped like a hemisphere made of solid glass, so she wants to design a box to keep it in
so it won't get broken. Her paperweight has a radius of 3 cm.
What should the dimensions of
the inside of box be so the box is
as small as possible?
Answer:
6 x 6 x 3 cm
Step-by-step explanation:
The base of the box needs to fit the base of the hemisphere.
The maximum width and length of the hemisphere is the diameter of the base of the hemisphere (which is circular)
Diameter of a circle = 2r
As the radius = 3 cm, the diameter = 2 x 3 = 6 cm
Therefore, the width and length of the box should both be 6cm
The height of the box needs to accommodate the height of the hemisphere. The height of the hemisphere is the radius, so the height of the box should be 3 cm.
Therefore, the dimensions of the box should be 6 x 6 x 3 cm
A movie theater has a seating capacity of 167. The theater charges $5.00 for children, $7.00 for students, and $12.00 for adults. There are half as many adults as there are children. If the total ticket sales was $ 1198, How many children, students, and adults attended?
Child attend:
Student attend:
Adult attend:
Answer:
Child attend: 58
Studen attend: 80
Adult attend: 29
Step-by-step explanation:
a + c + s = 167 Eq. 1
12a + 5c + 7s = 1198 Eq. 2
a = c/2 Eq. 3
a = adult attend
c = children attend
s = students attend
Replacing Eq, 3 in Eq. 2:
12(c/2) + 5c + 7s = 1198
6c + 5c + 7s = 1198
11c + 7s = 1198
7s = 1198 - 11c
s = (1198 - 11c) / 7 Eq, 4
Replacing Eq, 3 and Eq, 4 in Eq, 1
c/2 + c + (1198-11c) / 7 = 167
7c/14 + 14c/14 + 2(1198-11c)/14 = 2338/14
7c/14 + 14c/14 + 2396/14 - 22c/14 = 2338/14
7c + 14c + 2396 - 22c = 2338
7c + 14c - 22c = 2338 - 2396
-1c = -58
c = -58/-1
c = 58
from Eq. 3
a = c/2
a = 58/2
a = 29
from Eq. 4
s = (1198-11c)/7
s = (1198 - 11*58)/7
s = (1198 - 638) / 7
s = 560/7
s = 80
Check:
from Eq, 1
58 + 29 + 80 = 167
Find two square numbers that total 45
what is 13,931 rounding by 10
Answer:
13,930
Habe ein gut tag.
PLEASE HELP ILL GIVE BRAINLIEST
Answer:
x = 6
Step-by-step explanation:
first find the angle
51 + 72 + x = 180
123 + x = 180
x = 180 - 123
x = 57
so the third angle is 57
now find the value of x in the given expression
8x + 9 = 57
8x = 57 - 9
8x = 48
x = 48/8
x = 6
now check whether the value of x is correct or not by evaluating the value of x in expression
8x + 9 = 57
8(6) + 9 = 57
48 + 9 = 57
57 = 57
so its true
Method 2
51 + 72 + (8x + 9) = 180
123 + 8x + 9 = 180
132 + 8x = 180
8x = 180-132
8x = 48
x = 48/8
x = 6
now again you can check by evaluating the value of x in the above expression
Find the area of the circle if the square has an area of 900 in.² to give your answer in terms of
Diameter of circle = length of each side of the square
The formula for calculating the area of a square is
Area = l^2
where l is the length of each side
From the information given,
Area = 900
900 = l^2
l = √900
l = 30
diameter = 30
radius = diameter/2 = 30/2
radius = 15
The formula for calculating the area of a circle is
Area = πr^2 = π * 15^2
Area of circle = 225π in^2
Congruent Triangle Proofs. List reasons for the statements. Prove PQR congruent to STR and prove JKL is congruent to NKM 35 points!!
We proved that ΔPQR congruent to ΔSTR and ΔJKL is congruent to ΔNKM using the given conditions.
What are congruent traingles?
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. If pairings of corresponding sides and corresponding angles are equal, two triangles are said to be congruent. They are the exact same size and form. It is necessary for both triangles to be superimposed on one another.
1) Consider triangles ΔPQR and ΔSTR
PQ ≅ ST - Given
QR ≅ TR - Given
R is the midpoint of PS - Given
PR ≅ SR - Since R is the midpoint it cuts line PS equally
ΔPQR ≅ ΔSTR - Since the corresponding sides of the triangles are equal, they are congruent triangles.
2) Consider triangles ΔJKL and ΔNKM
JL ≅ NM - Given
K is the midpoint of JN and LM - Given
JK ≅ NK - Since K is the midpoint it cuts line JN equally
LK ≅ MK - Since K is the midpoint it cuts the line LM equally
ΔJKL ≅ ΔNKM - Since the corresponding sides of the triangles are equal, they are congruent triangles.
Therefore we proved that ΔPQR congruent to ΔSTR and ΔJKL is congruent to ΔNKM using the given conditions.
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Which pair of functions is not a pair of inverse functions?
Answer:
the answer is D
the inverse should be -20x/x-1
and thank you i didnt know that the of f(x)=x⁵
is ⁵√x
(~ ̄³ ̄)~
X is carrying out a series of experiments which involve using increasing amounts of a chemical. In the first experiment he uses 6g of the chemical and in the second experiment he uses 7.8g of the chemical.
(i) Given that the amounts of the chemical used form an arithmetic progression, find the total amount of chemical used in the first 30 experiments. [4]
(ii) Instead it is given that the amounts of the chemical used form a geometric progression. X has a total of 1800g of the chemical available. Show that N, the greatest number of experiments possible, satisfies the inequality
1.3N ≤ 91.
and use logarithms to calculate the value of N.
Answer:
a) 963g
b) 17
Step-by-step explanation:
i) Now we must first find the common difference of the AP
d = 7.8 -6 = 1.8
Now the sum of the AP gives the total amount of chemical used for 30 experiments
Sn = n/2 [2a + (n-1)d]
n= 30, a = 6, d= 1.8
Sn = 30/2[2(6) + (30-1) (1.8)]
Sn = 15[12 + 52.2]
Sn = 963g
ii)For the G.P the common ration is (r)= 7.8/6 = 1.3
Since r>1, sum of GP = a (r^n -1)/r-1
If sum = 1800g
1800= 6(1.3^n -1)/1.3 - 1
1800 = 6(1.3^n -1)/0.3
1800 * 0.3 = 6(1.3^n -1)
540 = 6(1.3^n -1)
540/6 = (1.3^n -1)
90 = 1.3^n -1
90 + 1 = 1.3^n
1.3^n = 91
log 1.3^n = log 91
nlog1.3 = log 91
n = log91/log 1.3
n = 1.959/0.114
n = 17
Answer:
a) 963g
b) 17
Step-by-step explanation:
i) Now we must first find the common difference of the AP
d = 7.8 -6 = 1.8
Now the sum of the AP gives the total amount of chemical used for 30 experiments
Sn = n/2 [2a + (n-1)d]
n= 30, a = 6, d= 1.8
Sn = 30/2[2(6) + (30-1) (1.8)]
Sn = 15[12 + 52.2]
Sn = 963g
ii)For the G.P the common ration is (r)= 7.8/6 = 1.3
Since r>1, sum of GP = a (r^n -1)/r-1
If sum = 1800g
1800= 6(1.3^n -1)/1.3 - 1
1800 = 6(1.3^n -1)/0.3
1800 * 0.3 = 6(1.3^n -1)
540 = 6(1.3^n -1)
540/6 = (1.3^n -1)
90 = 1.3^n -1
90 + 1 = 1.3^n
1.3^n = 91
log 1.3^n = log 91
nlog1.3 = log 91
n = log91/log 1.3
n = 1.959/0.114
n = 17
a basketball team wants to paint half of a free-throw circle grey. If the circumference of the free-throw circle is 30.77 feet, what is the are, in square feet, that will be painted grey? use 3.14 for PI, and round to the nearest square foot.
The area that will be painted grey is approximately 38 ft².
The circumference of the free-throw circle is given as 30.77 feet, and we know that the free-throw circle is a perfect circle. We can use the formula for circumference to find the radius of the circle, which will be necessary to calculate its area.
Circumference of a circle = 2πr
30.77 = 2 x 3.14 x r
r = 30.77 / (2 x 3.14) = 4.9 feet
Half of the circle will be painted grey. Find the area of half the circle using the formula for the area of a circle.
Area of a circle = π x r²
Area of half the circle = 0.5 x π x r²
Area of half the circle = 0.5 x 3.14 x 4.9²
Area of half the circle = 37.73 ft²
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please help i worked on this for a long time and i cant figure it out.
I am NOT in collage btw
Answer:
Do you need to be in college? I´m pretty sure it does not affect anything uwu
Step-by-step explanation:
Find the sum of 0.2126 and 0.7145 correct to 3 significant figures
Answer:
0.927
Step-by-step explanation:
add then round the last digit (it doesnt matter if it is a decimal number or not).
2) Ayanda wants to invest R200 000. The bank offers him 2 options for his
6 year investment.
Option 1: 12% Simple interest p.a.
Option 2: 9,5% Compound interest p.a.
4.2.1) Calculate the return on Ayanda's investment using Option 1.
●
●
4.2.2) Calculate the return on Ayanda's investment using Option 2.
4.2.3) Which option will render the most money?
Answer:
4.2.1) R140 000
4.2.2) R144 758.28
4.2.3) Option 2
Step-by-step explanation:
To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.
\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)
Given values:
P = R200 000r = 12% = 0.12t = 6 yearsSubstitute the given values into the formula and solve for I:
\(I=200000 \cdot 0.12 \cdot 6\)
\(I=24000 \cdot 6\)
\(I=144000\)
Therefore, the return on Ayanda's investment using Option 1 is R144000.
\(\hrulefill\)
To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.
\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)
Given values:
P = R200 000r = 9.5% = 0.095t = 6 yearsSubstitute the given values into the formula and solve for I:
\(I=200000(1+0.095)^6-200000\)
\(I=200000(1.095)^6-200000\)
\(I=200000(1.72379142...)-200000\)
\(I=344758.28426...-200000\)
\(I=144758.28426...\)
\(I=144758.28\)
Therefore, the return on Ayanda's investment using Option 2 is R144758.28.
\(\hrulefill\)
Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.
A university is interested in determining the average statistics anxiety score for all undergraduate students in the U.S. For a random sample of 33 undergraduate students, it is found that the average average statistics anxiety score is 39.4 with a standard deviation of 0.9. Assume that the statistics anxiety scores for all undergraduate students in the U.S is normally distributed. A 98% confidence interval for the true mean statistics anxiety score μ is closest to.
The 98% confidence interval for the true mean statistics anxiety score (μ) is approximately (39.037, 39.763).
To calculate the 98% confidence interval for the true mean statistics anxiety score (μ) for all undergraduate students in the U.S., we can use the formula:
Confidence interval = sample mean ± (critical value * standard error)
First, we need to find the critical value associated with a 98% confidence level. Since we are assuming a normal distribution, we can use the Z-table or a statistical software to find this value. For a 98% confidence level, the critical value is approximately 2.33.
Next, we calculate the standard error (SE) using the formula:
SE = standard deviation / √sample size
In this case, the standard deviation is 0.9 and the sample size is 33. Plugging these values into the formula, we get: SE = 0.9 / √33 ≈ 0.156
Now, we can calculate the confidence interval:Confidence interval = 39.4 ± (2.33 * 0.156)
Simplifying the expression:Confidence interval ≈ 39.4 ± 0.363
This gives us the interval (39.037, 39.763). This means we are 98% confident that the true mean statistics anxiety score for all undergraduate students in the U.S. falls within this interval.
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PLEASE HELP!!! WILL GIVE BRAINLIEST!!!
A package is in the shape of a triangular prism. The bases are right triangles with perpendicular legs measuring 9 centimeters and 12 centimeters. The distance between the bases is 10 centimeters.
What is the surface area of the triangular prism?
210 square centimeters
318 square centimeters
360 square centimeters
468 square centimeters
Answer:
Step-by-step explanation:
Area of base = 0.5×9×12 = 54 cm²
Hypotenuse of base = √(9²+12²) = 15
Lateral surface area = 10(9+12+15) = 360 cm²
Total surface area = 2×54 + 360 = 468 cm²
1. Find the mean, median, mode, and range of
the following set of data: 1,2,4,6,4,4
Step-by-step explanation:
the median is 4
the mean is 1+2+4+6+4+4/6
21/6=7\2
6.5 the mode is 4
My sister and I are buying a television for our room. Because I am older, I will pay $45 more than my sister. If the television costs $299, then how much does my sister have to pay.
What is the approximate length of side GF in triangle EFG?
Answer:
41.93 degrees
Step-by-step explanation:
convert 62/80 to a decimal and to a percent
1
Jane bought a car for £24000
2 years later she sold it for £26000
Work out her percentage profit to 1
decimal place
Formula for Profit Percentage = (Profit/C.P.) 100Where C.P. denotes the article's cost price, i.e. the price at which the article was originally purchased.
Jane bought a car for £24000
she sold it for £26000
profit = 2000
profit percentage = 2000/26000 x100 = 7.7%
What is the Profit Percentage Formula?Profit is always calculated using the cost price. The following formula is used to calculate the percentage of profit earned from a specific sale:Formula for Profit Percentage = (Profit/C.P.) 100Where C.P. denotes the article's cost price, i.e. the price at which the article was originally purchased.When a product's selling and cost prices are known, the profit can be calculated using the formula Profit = Selling Price - Cost Price. Following that, the profit percentage formula is Profit percentage = (Profit/Cost Price) 100.Here,
Jane bought a car for £24000
she sold it for £26000
profit = 2000
profit percentage = 2000/26000 x100 = 7.69%
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Amy invested $500 per month in a 401k that earned 6% annual return for 40 years. Hank invested $1,000 per month in a 401k that also earned 6% annual return, but for 20 years. Which of the following would be true?
Answer:
The correct option is a. Amy’s balance would be greater than Hank’s in the end.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
Amy invested $500 per month in a 401k that earned 6% annual return for 40 years. Hank invested $1,000 per month in a 401k that also earned 6% annual return, but for 20 years. Which of the following would be true?
a. Amy’s balance would be greater than Hank’s in the end.
b. Amy’s balance is $5,142 and Hank’s balance is $3,207.
c. Hank’s balance would be greater than Amy’s in the end.
d. The investment and balance would be the same.
e. None of these are true
The explanation to the answer is now given as follows:
The balance in the end for each can be determined using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:
FV = M * (((1 + r)^n - 1) / r) ................................. (1)
Where;
For Amy:
FV = Future value or balance in the end = ?
M = Monthly investment = $500
r = Monthly interest rate = 6% / 12 = 0.06 / 12 = 0.005
n = number of months the investment will be made = 40 years * 12 months = 480
Substituting the values into equation (1), we have:
FV = $500 * (((1 + 0.005)^480 - 1) / 0.005)
FV = $500 * 1,991.49
FV = $995,745.37
Therefore, Amy’s balance would be $995,745.37 in the end.
For Hank:
FV = Future value or balance in the end = ?
M = Monthly investment = $1,000
r = Monthly interest rate = 6% / 12 = 0.06 / 12 = 0.005
n = number of months the investment will be made = 20 years * 12 months = 240
Substituting the values into equation (1), we have:
FV = $1,000 * (((1 + 0.005)^240 - 1) / 0.005)
FV = $1,000 * 462.04
FV = $462,040.90
Therefore, Hank’s balance would be $462,040.90 in the end.
Conclusion
Since Amy’s balance of $995,745.37 is greater than Hank’s balance $462,040.90, it therefore implies that the correct option is a. Amy’s balance would be greater than Hank’s in the end.
Find the value of x plsss
Answer:
x=10.8
Step-by-step explanation:
9²+6²=c²
81+36=c²
117=c²
√117=10.81
x=10.81
Which amount of money is closest to the 15% tip?
$3.00
$3.50
$4.00
$4.50
Jill has 4 one-dollar bills, 3 quarters, 4 dimes, and 3 pennies. Mark has 3 one-dollar bills,
4 dimes, and 2 pennies. What is the difference between the amount of money Jill has and
the amount of money Mark has?
Answer:
1 dollar 3 quarters 1 penny
Step-by-step explanation:
The difference between the amount of money Jill has and the amount of money Mark has, is $1.74.
What is addition?In addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms "addends" and "sum" refer to the numbers that are added and the result of the operation, respectively.
One-dollar is the 100-cent coin
The dime is the 10-cent coin.
Quarters is the 100/ 4 = 25-cent coin.
And a one-cent coin is a penny.
Given:
Jill has 4 one-dollar bills, 3 quarters, 4 dimes, and 3 pennies.
Total = 4 + 0.75 + 0.40 + 0.01
Total = $5.16
Mark has 3 one-dollar bills, 4 dimes, and 2 pennies.
Total = 3 + 0.40 + 0.02
Total = $3.42
The difference between the amount of money Jill has and the amount of money Mark has = $5.16 - $3.42 = $1.74
Therefore, the difference is $1.74.
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Michael went to the game store there was so much games he wanted and if one of them was $42.29 and the other one was $87.99 and he had $142 how much would he have left
Answer:
$11.72
Step-by-step explanation:
Add: $42.29 + $87.99 = $130.28
Subtract: $142 - $130.28 = $11.72
Answer:
he would have spent 131.08 dollars meaning he has 11.72 dollars left.
Step-by-step explanation:
I NEED AN ANSWER!! PLEASE
Solve for x: 5(x + 3) = 4(x − 3) (1 point) −18 −27 −3 −6
Answer:
\(-27\)
Step-by-step explanation:
\(5(x+3)=4(x-3) \\ \\ 5x+15=4x-12 \\ \\ x+15=-12 \\ \\ x=-27\)
Convert the rectangular coordinates (5,−5√3) to polar form. Let r>0 and 0≤θ<2π.
Enter your answer by filling in the boxes. Enter coordinates as simplifed fractions or radicals in simplest form.
( , )
Answer:
(10, 5π/3)
Step-by-step explanation:
To convert rectangular coordinates (5, -5√3) to polar form, we can use the following formulas:
r = √(x^2 + y^2)
θ = arctan(y/x)
Substituting the given values, we get:
r = √(5^2 + (-5√3)^2) = √(25 + 75) = √100 = 10
θ = arctan((-5√3)/5) = arctan(-√3) = -π/3
Note that the value of θ is in the fourth quadrant, which corresponds to a negative angle. However, we need to express the angle θ in the range 0 ≤ θ < 2π. To do this, we can add 2π to the angle if it is negative:
θ = -π/3 + 2π = (5π/3)
Therefore, the rectangular coordinates (5, -5√3) in polar form are (10, 5π/3).
Solve A=Q + ms for Q.
Answer:
couldnt tell ya
Step-by-step explanation:
not enough info
- I made this IMPOSSIBLE Question to see who can answer it correctly
(GIVING BRAINLIEST) Reporting trolls ( reports=points loss)
Answer:
converse 3
contrapositive 1
inverse 2
conditional statement 4
Answer:
i dont know
Step-by-step explanation:
you got me good just sayian
(pls dont report i beg)
a owner increases the rent office house by 5% at end of each year if current its rent is ₹2500pm how much will be the rent after two years
Answer:
2950$
Step-by-step explanation:
2500×5%=125$
125×2=250$
2500+250=3960$