===================================================
Explanation:
G = amount of money George starts with
T = amount of money Tia starts with
Initially the ratio of their money is 9:4 so G/T = 9/4. Solve for G to get G = (9/4)T.
--------
After George spends 24 dollars he's left with (G-24) dollars. Tia gains 11 dollars so she has (T+11) dollars. They have the same amount of money after these two events occur, so G-24 = T+11.
Plug in G = (9/4)T and solve for T
G-24 = T+11
(9/4)T-24 = T+11 ... replace G with (9/4)T
4*[ (9/4)T-24 ] = 4*[ T+11 ] ... multiply both sides by 4 to clear out fraction
9T - 96 = 4T + 44 ... distribute
9T - 4T = 44 + 96
5T = 140
T = 140/5
T = 28
Tia started off with 28 dollars. We could stop here because your teacher is only asking about Tia's initial amount.
----------
If you want to find how much George started with, then plug T = 28 into G = (9/4)T to get...
G = (9/4)T
G = (9/4)*28
G = 2.25*28
G = 63
George started off with 63 dollars
The ratio of 63:28 reduces to 9:4 after dividing both parts by the GCF 7. This confirms the first fact we're given.
Notice how 63 drops to 63-24 = 39 after George spends $24. At the same time, Tia's amount increases to 28+11 = 39, which is the same as George's updated amount. Both facts match the description, so we have confirmed the answer.
Answer:
$28
Step-by-step explanation:
What is the slope of the line segment? A graph is shown. The values on the x axis are 0, 1, 2, 3, 4, and 5. The values on the y axis are 0, 4, 8, 12, 16, and 20. A straight line joining the ordered pairs 0, 0 and 1, 4 and 2, 8 and 3, 12 and 4, 16.
Answer:
4
Step-by-step explanation:
The coordinates are: A(0,0), B(1,4), C(2,8), D(3,12), E(4,16)
Using coordinates B and D, slope = (12 - 4)/(3 - 1) = 8/2
∴ slope = 4
Answer:
4
Step-by-step explanation:
The vertices of a triangle are A(0,3) B(-2,-4) and C(1,5) find the new vertices
Use the rule (x,y) (x-2,y+4) to translate each vertex.
Answer:
see explanation
Step-by-step explanation:
Using the translation rule (x, y ) → (x - 2, y + 4 )
Subtract 2 from the original x- coordinate and add 4 to the original y- coordinate, thus
A(0, 3 ) → A'(0 - 2, 3 + 4 ) → A'(- 2, 7 )
B(- 2, - 4 ) → B'(- 2 - 2, - 4 + 4 ) → B'(- 4, 0 )
C(1, 5 ) → C'(1 - 2, 5 + 4 ) → C'(- 1, 9 )
Hi May I know how to solve this with step by step explanation please
Answer:
13.33 cm
Step-by-step explanation:
Given, ratio of volumes v ÷ V = 8 ÷ 27
This ratio is applicable to heights of same containers, as the volume is directly proportional with height (V=Ah, A- base, h- height)
So we have:
h ÷ H = 8 ÷ 27and
H=45 cmThen,
h ÷ 45 = 8 ÷ 27h = 45 × 8/27h = 40/3 = 13.33 cmAnswer:
13.33 cm
Step-by-step explanation:
Down here.
the hypotnuse of a 45 -45 -90 triangle measures 22√2 units. what is the length of the leg of the triangle?
Answer:
22 units.
Step-by-step explanation:
In 45- 45- 90 triangles, there is a 1 to 1 to the square root of 2 formula. Each side length measures 1x, while the hypotenuse measures x times the square root of 2.
In this case, the hypotenuse measures 22 and the square root of 2 units. To find the value of x, simply divide that by the square root of 2 units, and you get x = 22 units. Multiply that by 1, and you get 22 units, which is the length of the leg of the triangle.
Hope this helps!
Determine whether the study is an observational study or an experiment.
Research is conducted to determine if there is a relation between hearing loss and exposure to mumps. Does the description correspond to an observational study or an experiment?
Researchers are observing those with mumps to see how it affects hearing loss at all. There may be strong correlation, weak correlation, or no correlation at all.
With an experiment, researchers would break the participants into two groups: control group and treatment group. Those in the control group get the placebo (fake treatment) while the treatment group gets the treatment applied to them. If we were dealing with an experiment for this context, then the treatment group would get exposed to mumps on purpose. Of course, this is unethical and dangerous so an experiment for this type of project is not a good idea. It's better to go with an observational study.
Please answer ASAP. The question is down below.
Answer: 1) c 2) d
Step-by-step explanation:
Use Pythagorean Theorem to find the hypotenuse (r): x² + y² = r²
Given: x = 2, y = 6
2² + 6² = r²
4 + 36 = r²
40 = r²
[tex]\sqrt{40}=r[/tex]
[tex]\sin \theta=\dfrac{y}{r}\quad =\large\boxed{\dfrac{6}{\sqrt{40}}}\quad \rightarrow \dfrac{6}{2\sqrt{10}}\quad \rightarrow \dfrac{3}{\sqrt{10}}[/tex]
*******************************************************************************************
[tex]\sin \theta = \dfrac{opposite(y)}{hypotenuse(r)}\quad =\dfrac{12}{20}\quad \rightarrow \dfrac{3}{5}\quad \rightarrow \large\boxed{0.6}\\\\\\\cos \theta = \dfrac{adjacent(x)}{hypotenuse(r)}\quad =\dfrac{16}{20}\quad \rightarrow \dfrac{4}{5}\quad \rightarrow \large\boxed{0.8}[/tex]
How many times larger is 74 than 30?
Answer:
approximately 2.46
Step-by-step explanation:
Answer:
2.4666666666
Step-by-step explanation:
To Find How Much Larger Or Smaller Any Given Number Is To Another, Do (#1)/(#2). In This Case, 74/30 Into Google Does A Quick Job Of This Question!
How many minutes are in 15 hours?
Answer:
900
Step-by-step explanation:
15 TIMES 60 IS 900
Hi there! Hopefully this helps!
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Answer: There are 900 minutes in 15 hours.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Since there are 60 minutes in each hour, we need to multiply the time value by 60. Like this:
15 x 60 = 900.
Find an equation of the line that passes through the point (2, 1) and
is perpendicular to the line x + 2y=-2
Answer:
2x - y = 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
x + 2y = - 2 ( subtract x from both sides )
2y = - x - 2 ( divide all terms by 2 )
y = - [tex]\frac{1}{2}[/tex] x - 1 ← in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2 , thus
y = 2x + c ← is the partial equation
To find c substitute (2, 1) into the partial equation
1 = 4 + c ⇒ c = 1 - 4 = - 3
y = 2x - 3 ← equation in slope- intercept form
add 3 to both sides
y + 3 = 2x ( subtract y from both sides )
3 = 2x - y, thus
2x - y = 3 ← equation in standard form
]
NEED HELP ASAP!! IF YOU KNOW HOW TO DO IT GO AHEAD BUT IF YOU DONT, DONT ANSWER
Answer:
the second one.its a parallelogram
help me out with a and b
i Will give brainliest and follow you back if you answer first.
Answer:
Step-by-step explanation:
A = {2,8,10,14}
B= {6,8,20}
C={8,18,20,24}
A ∩ B --> intersection means elements that are in both sets A & B
A ∩ B = {8}
A∩ C = {8}
B ∩ C = {8 , 20}
A∩B ∩ C = {8}
First blue box = { 2,10, 14}
Second blue box = {18, 24}
First green box = { 8}
Second green box = { 20}
b) A ∩ B = {8}
n [ A ∩ B] = 1
Probability of the number to be a member of A∩B = 1 / 25
Give the coordinates of each vertex (D, E, and F) and explain how you found the coordinates.
Answer:
D(-4, -3), E(-7, 4), and F(-7, -3).
Step-by-step explanation:
The current coordinates are A(4, 2), B(7, 9), and C(7, 2).
If you reflect the coordinates over the y-axis, the y-values will not be changing, but the signs of the x-values will flip. So, you will have A'(-4, 2), B'(-7, 9), and C'(-7, 2).
When you translate the resulting triangle down 5 units, the y-values will decrease by 5 units. So, the coordinates of triangle DEF will be D(-4, -3), E(-7, 4), and F(-7, -3).
Hope this helps!
Answer:
D (-4, -3)
E (-7, 4)
F (-7,-3)
Step-by-step explanation:
Well triangle ABC reflected over the y-axis to make triangle DEF looks like the image below. ↓
Then we have to translate triangle DEF 5 units down.
With the coordinates D, E, F,
D (-4,2)
E (-7,9)
F (-7,2)
To translate it 5 units down we just subtract the y coordinates by 5.
D (-4, -3)
E (-7, 4)
F (-7,-3)
Thus,
the coordinates for triangle DEF are (-4, -3) , (-7, 4) , (-7,-3).
Hope this helps :)
You build 7 model airplanes during the summer. At the end of the summer, you have 25 model airplanes. How many model airplanes did you have before the summer? Select the correct equation and solution. Check the solution.
Answer:
18
Step-by-step explanation:
You have 25 when you are done, but you made 7, so subtract that from 27.
25-7 equals 18.
help me plzzzzz help
Answer:
90000 km
Step-by-step explanation:
1 hour = 3600 sec
distance = speed x time
= 25 km/s x 3600 s
= 90000 km
standard form = 9 x 10⁴
An icicle is in the shape of an inverted cone with a diameter of 14 mm and a height of 60 mm. How much frozen water
is in the icicle? Use 3.14 for Round the answer to the nearest tenth
A 188.4 mm
B 980.0 mm
C 3,077.2 mm
D 9,231.6 mm
Answer:
Option C. 3077.2 mm³
Step-by-step explanation:
Data obtained from the question include the following:
Diameter (d) = 17 mm
Height (h) = 60 mm
Pi (π) = 3.14
Volume =?
Next, we shall determine the radius of the cone. This is illustrated below:
Diameter (d) = 17 mm
Radius (r) =.?
Radius (r) = diameter (d)/2
r = d/2
r = 14/2
r = 7 mm.
The radius therefore, is 7 mm.
To know how much frozen water
is in the icicle, we shall calculate the volume of the icicle using the formula for calculating the volume of a cone. This is illustrated below:
Height (h) = 60 mm
Pi (π) = 3.14
Radius (r) = 7 mm
Volume =..?
V = ⅓πr²h
V = ⅓ × 3.14 × 7² × 60
V = 3.14 × 49 × 20
V = 3077.2 mm³
Therefore, the amount of frozen water in the icicle is 3077.2 mm³
Answer:
C 3,077.2 mm
Step-by-step explanation:
You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 99.9% confident that you estimate is within 1% of the true population proportion. How large of a sample size is required
Answer: 27061
Step-by-step explanation:
given that Р = 0.5
so
1 - P = 1 - 0.5 = 0.5
ERROR OF MARGIN E = 0.01
SIGNIFICANCE LEVEL α = 1 - confidence level
α = [(1 - (99.9/100)] = 0.0010
α / 2 = 0.001 / 2 = 0.0005
Zα/2 = Z0.0005 = 3.29 (using the Z table )
therefore
Sample size n = ((Zα/2) / E)² * P * (1 - P )
Sample size n = (3.29 / 0.01)² * 0.5 * 0.5
Sample size n = 108,241 * 0.5 * 0.5
Sample size n = 27,060.25 ≈ 27,061
Answer:
sample size should be atleast n= 27069
Step-by-step explanation:
Given that,
confident level(CI) = 99%= 0.999
desired marginal error=1%= 0.01
note: marginal error = length of CL/2
significant level α = 1 - confident level = 1 - 0.999= 0.001
critical value = Zα/2 = Z(0.001/2) = Z0.0005( value of from z table) = 3.2905267
since we don't have preliminary estimate, p' = 0.5, which is require for maximum value
n = p' × (1 - p')(critical value/desired marginal)²
n= 0.5 × 0.5(3.2905267/0.01)²
n = 27068.91
the value of n has to be an integer = 27069
Please help ASAP! If correct will mark brainliest
Answer:
5
Step-by-step explanation:
We need to find the value of AP
First, lets compare the perimeters:
P_ABC= AB+BC+AC= 45P_ABP= AB+BP+AP = 25P_APC= AP+AC+PC= 30Sum of the perimeters of smaller triangles:
P_ABP+P_APC= AB+BP+AP+ AP+AC+PCAs BP+PC= BC we can put it as:
AB + BC +AC + 2APand
P_ABC+2APPlug in values of perimeters:
25+30= 45+ 2AP2AP= 10AP= 10/2AP= 5Answer is: 5
The volume of the Atlantic Ocean is about 3.1⋅10173.1 \cdot 10^{17}3.1⋅10173, point, 1, dot, 10, start superscript, 17, end superscript cubic meters. The Mississippi River has an annual flow of 6.3⋅10116.3 \cdot 10^{11}6.3⋅10116, point, 3, dot, 10, start superscript, 11, end superscript cubic meters. how many times would the annual flow of the mississippi river fit in the atlantic ocean? write your final answer in scientific notation, and round to two decimal places.
Answer: The annual flow of the Mississippi river would fit in the Atlantic ocean [tex]4.92\times10^5[/tex] times.
Step-by-step explanation:
Given: Volume of Atlantic Ocean= [tex]3.1\times10^{17}[/tex] cubic meters
Annual flow of Mississippi river = [tex]6.3\times10^{11}[/tex] cubic meters.
then, the number of times the annual flow of the Mississippi river would fit in the Atlantic ocean = [tex]\dfrac{\text{ Volume of Atlantic Ocean}}{\text{Annual flow of Mississippi river}}[/tex]
[tex]=\dfrac{3.1\times10^{17}}{6.3\times10^{11}}\ \ \=0.492063492063\times10^{17-11}\ \ [\dfrac{a^m}{a^n}=a^{m-n}]\\\\=0.492063492063\times10^6\approx4.92\times10^5[/tex]
Hence, the annual flow of the Mississippi river would fit in the Atlantic ocean [tex]4.92\times10^5[/tex] times.
Best answer will be rated brainliest
Answer:
A. 6 and 30
B. 8 and 28
Step-by-step explanation:
we know that the area of the three squares must satisfy the Pythagorean Theorem so c² = a² + b²
where
c² is the area of the largest square
a² and b² are the areas of the smaller squares
now.. 36² = a² + b2
The sum of the areas of the smaller squares must be equal to 36
therefore
6 and 30 >>>> could be the areas of the smaller squares (6 + 30 = 36)
8 and 28 >>>> could be the areas of the smaller squares (8 + 28 = 36)
hope it clears your mind.
Please mark as the brainliest
Determine the angles of rotation. Please answer!!!
Answer:
total rotation = 90 clockwise.
Step-by-step explanation:
Rotation from B to negative y-axis = 45 degrees because B(-3,-3)
Rotation from negative y-axis to B' = 45 degrees because B(-3,3)
Therefore total rotation = 45+45 = 90 clockwise.
2
What is the solution of the equation 6x - 3 = -51?
A. -9
B. -8
c. 8.
D. 9
Answer:
x = -8
Step-by-step explanation:
6x - 3 = -51
Add 3 to each side
6x - 3+3 = -51+3
6x = -48
Divide each side by 6
6x/6 = -48/6
x = -8
Find two national number
between 2 and 3
Answer:
The answer is 2.5
Step-by-step explanation:
Formula Used is is ½ x x+y
so it is ½ x 2 + 3
½ x 5 = 2.5
Answer:
2=2/1
3=3/1
multiplying both fractions by 10.
2*10/1*10
3*10/1*10
20/10 and 30/10
so nos are 21/10.......29/10
What else would need to be congruent to show that ABC= ADEF by SAS?
A. ZCE ZF
B. BC = EF
O C. ZA= ZD
D. AC = DF
Answer:
Option C.
Step-by-step explanation:
It is given that,
[tex]\overline{AB}\cong \overline {DE}[/tex]
[tex]\overline{AC}\cong \overline {DF}[/tex]
According to SAS congruence property, two triangles are congruent if they have two congruent corresponding sides and their included angles are congruent.
Angle between [tex]\overline{AB}\text{ and }\overline {AC}[/tex] is [tex]\angle A[/tex].
Angle between [tex]\overline{DE}\text{ and }\overline {DF}[/tex] is [tex]\angle D[/tex].
So, [tex]\Delta ABC\cong \Delta DE F[/tex] by SAS, if
[tex]\angle A\cong \angle D[/tex]
Therefore, the correct option is C.
Find the mean of the following data set. 8, 5, 15, 12, 10 12.5 10 14 50
Answer:
10
Step-by-step explanation:
8+5+15+12+10= 50 / 5 = 10
Simplify the expression: (− 2/3 pq^4)^2·(−27p^5q)
Answer:
-12p^7q^9
Step-by-step explanation
-\left(-\frac{2}{3}pq^4\right)^2\cdot \:27p^5q
-27\cdot \frac{2^2p^2q^8}{3^2}p^5q
Multiply the fractions
\frac{2^2p^2q^8\cdot \:27p^5q}{3^2}
-\frac{2^2\cdot \:27p^7q^9}{3^2}
-2^2\cdot \:3p^7q^9
Translate into an algebraic expression and simplify if possible. C It would take Maya x minutes to rake the leaves and Carla y minutes, what portion of the leaves do they rake in one minute if they work together?
Answer:
in one minute they rake [tex]\frac{y+x}{xy}[/tex] leaves working together.
Step-by-step explanation:
If Maya rakes the leaves in x minutes, then, in one minute she rakes [tex]\frac{1}{x}[/tex] leaves.
In the case of Carla, if she rakes the leaves in y minutes, in one minute she rakes [tex]\frac{1}{y}[/tex] leaves.
Therefore, to know the portion of leaves they can rake in one minute working together, we need to sum up both of the portions each one of them rake in one minute, this gives us: [tex]\frac{1}{x}+ \frac{1}{y}[/tex]
Now, to simplify this expression:
[tex]\frac{1}{x}+ \frac{1}{y} =\frac{y+x}{xy}[/tex]
Thus, in one minute they rake [tex]\frac{y+x}{xy}[/tex] leaves.
Segment MP is a diameter of circle O.
Which equation can be used to find mMN?
N
O MMN + 150 = 180
M
O MMN + 150 = 360
150°
O MMN - 150 = 180
OmMN – 150 = 360
a
Answer:
mMN + 150 = 180
Step-by-step explanation:
Circle O is shown. Line segment M P is a diameter. Line segment N O is a radius. Angle N O P is 150 degrees.
Given that:
NO is the radius and ∠NOP = 150°.
The angle addition postulate which states that a larger angle is formed when two smaller angles are placed side by side. If two angle x and y are small angles placed side by side, a big angle Z formed is given as:
z = x + y.
Therefore in circle O, using angle addition postulate:
mMN + ∠NOP = mMP
But mMP = 180° (angle on a straight line)
mMN + ∠NOP = 180°
mMN + 150 = 180
Find the m∠CDE rjrsjrsrjr
Answer:
m∠CDE = 60°
Step-by-step explanation:
Given that the arc at the center = 2 times the arc at the circumference, we have;
Angle at the center = arc CE = 120°
Whereby the angle at the circumference is given as m∠CDE and it is opposite the circle arc CE
We note that m∠CDE is the acute angle between chord DC and DE
Therefore, we have;
Angle at the center = 120° = 2 times the arc at the circumference = 2 × m∠CDE
120° = 2 × m∠CDE
m∠CDE = 120/2 = 60°
Therefore the angle of m∠CDE is equal to 60°.
YO PLZ HELP!! MARKING BRAINIEST!!
Answer:
x = 26, 16
Step-by-step explanation:
( x-21) ^2 = 25
Take the square root of each side
sqrt(( x-21) ^2) = ±sqrt(25)
x-21 = ±5
Add 21 to each side
x-21+21 = 21±5
x = 21±5
x = 21+5 and x = 21-5
x = 26, 16
Which of the expressions below can be factored using the difference of squares method?
A. 9x^2 - 16y2
B. 9x-16y
C. 9x^2 + 1672
D. 9x + 16y
Answer: A. [tex]9x^2 - 16y^2[/tex] .
Step-by-step explanation:
A difference of squares problem is factored as :[tex]a^2 - b^2 = (a + b)(a - b)[/tex]For this both terms in the form of squares and a minus sign between them.From all the options only option A has both terms square and they minus sign between them.
Also, [tex]9x^2 - 16y^2= (3x)^2-(4y)^2=(3x+4y)(3x-4y)[/tex]
Here a= 3x and b= 4
Hence, the correct answer is A. [tex]9x^2 - 16y^2[/tex] .
Answer:
A
Step-by-step explanation: