Answer:
15.07 hours
Step-by-step explanation:
The given relationship lets us write an equation in that uses rates in terms of tasks per hour. Let 'a' represent the number of hours it takes the assistant to grade exams alone. Then (a-2) is the number of hours it takes the experienced teacher. Working together, their total rate is ...
1/a + 1/(a-2) = 1/7 . . . . . . . tasks per hour
7(a -2) +7(a) = a(a -2) . . . . . multiply by 7a(a -2)
14a -14 = a^2 -2a . . . . . . . eliminate parentheses
a^2 -16a = -14 . . . . . . . . . subtract 14a
a^2 -16a +65 = 50 . . . . add 64 to complete the square
(a -8)^2 = 50 . . . . . . . write as a square
a -8 = ±5√2 . . . . . . take the square root
a = 8 +5√2 ≈ 15.072
It would take the teaching assistant about 15.07 hours to grade the exams alone.
_____
Additional comment
The quadratic also gives an extraneous solution of about 0.93 hours. This results in a negative task time for the experienced teacher. That solution makes no sense in the given scenario, so we ignored it.
5. Part A: Show another way to find the slope of the line that passes through the points listed in the table. Your way must be different from Avery's method.
. Part B: Justify why Avery's "divide y by x" method will not work to find the slope of every line and given an example (using a table, equation, or graph) in your justification
Answer:
The slope-intercept form
y = mx + bHere m is the slope and b is y-intercept
When b= 0
y = mxand
m = y/xIn this case Avery's method works
When b≠0
m = (y -b)/xIn this case Avery's method brings wrong outcome
Answer:
Step-by-step explanation:
A concrete truck loaded with concrete weighs up to 25 tons.
About how many pounds does the loaded truck weigh?
The loaded truck weighs
pounds.
Answer:
50,000 pounds
Step-by-step explanation:
1 ton = 2,000 pounds
How do I do this I’m stuck and I have no idea how to do this I’m very behind and need help
Step-by-step explanation:
I don't see all the options.
I only see the options under "angles", as it seems.
anyway, the way to prove this is :
the official definition of similar triangles is :
two triangles are said to be similar if their corresponding angles are congruent (and the corresponding sides are in proportion - but that is automatically true, when all 3 angles are matching).
so, if two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. we know this, because if two angle pairs are the same, then the third pair must also be equal (remember, the sum of all angles in a triangle is always 180°). When the three angle pairs are all equal, the three pairs of sides must also be in proportion.
now, we look at the 2 triangles.
the angles QPR and STR are congruent (the same size).
we know also the angles QRP and SRT : they are both 90° and therefore congruent.
and that means that also the third angles PQR and RST are equal and therefore congruent (due to the 180° sum rule).
so, we have all 3 pairs of angles to be congruent, and the two triangles are therefore similar.
The L.C.M of 16 and 18 is what? first person Brainliest answer
Answer:
144 is the l.c.m of 16 and 18
explanation:
multiples:
16 - 16, 32, 48, 64, 80, 96, 112, 128, 144
18 - 18, 36, 54, 72, 90, 108, 126, 144
Therefore, 144 is the l.c.m of 16 and 18 which is divisible by both numbers.
Answer:
144
Step-by-step explanation:
First, prime factorize the numbers.
16 = 2⁴
18 = 3² x 2
LCM (16, 18) = 2⁴ x 3²
= 16 x 9
= 144
Solution :-
144
100cm to 1 km in simplest form
Answer:
100cm = 0.001km
Step-by-step explanation:
100 divided by 100,000=0.001
Answer:
1/100th part of the whole part.
Step-by-step explanation:
Hope this helps :)
What is the GCF of 96 and 56??
A:14
B:2
C:8
D:16
Answer:
8
Step-by-step explanation:
Tanisha lives with her older sister and helps with the rent by paying $500 per month. Her annual salary as a child care specialist is $14,700 after taxes. Shopping is her favorite pasttime and loves buying new things, but she also wants to save money for her college classes. Select the budget that would best help meet her goals. Table A Monthly Budget Budget A Budget B Budget C Budget D Income $1,470 $1,225 $1,470 $1,225 Expenses - Rent Food.
Tanisha lives with her older sister and helps with the rent by paying $500 per month. Her annual salary as a child care specialist is $14,700 after taxes. So to save money for her college classes her monthly budget should be less than 725 .
What is budget ?Budget is total plan of income and expenditure of a period .
Here given that Her annual salary as a child care specialist is $14,700 after taxes. and she lives with her older sister and helps with the rent by paying $500 per month.
So money she have after rent can be calculated as:
[tex]14700-12\times500\\\\14700-6000\\\\=8700[/tex]
So her monthly saving after rent is
[tex]\frac{8700}{12} \\\\\\=725[/tex]
So her monthly budget should be less than 725
Tanisha lives with her older sister and helps with the rent by paying $500 per month. Her annual salary as a child care specialist is $14,700 after taxes. So to save money for her college classes her monthly budget should be less than 725 .
To learn more about budget visit :https://brainly.com/question/24940564
Answer:
B
Step-by-step explanation:
Edge 2022
have a great day!
L is the midpoint of MN¯¯¯¯¯¯¯, ML=2x+7 and LN=3x−3. Find ML, LN, and MN.
Answer:
[tex]ML=27\\LN=27\\MN=54[/tex]
Step-by-step explanation:
Since L is the midpoint of MN, by the definition of midpoint:
[tex]ML=LN[/tex]
We can picture the following segment:
M----------L----------N
We know that [tex]ML=2x+7[/tex] and [tex]LN=3x-3[/tex]. Since the two segments are equivalent, we can set them equal to each other:
[tex]2x+7=3x-3[/tex]
Now, let's solve for x. Subtract -7 from both sides:
[tex]2x=3x-10[/tex]
Subtract 3x from both sides:
[tex]-x=-10[/tex]
Divide both sides by -1:
[tex]x=10[/tex]
So, the value of x is 10.
With this, we can find the remaining lengths.
We know that ML is [tex]2x+7[/tex].
Substitute 10 for x. So, the length of ML is:
[tex]ML=2(10)+7=20+7=27[/tex]
We know that LN is [tex]3x-3[/tex]. So, the length of LN is:
[tex]LN=3(10)-3=30-3=27[/tex]
Finally, MN will be the combined lengths of ML and LN. So:
[tex]MN=ML+LN=27+27=54[/tex]
And we're done!
Answer:
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I’m slow at these stuff Please I’ll be so glad if someone help with this =^=
Answer:
the <5 = 28
because if u add <1 and <5 it will be a 180°
so....if u 180 - 152 ( which is the angle of 1< )
and
same goes to 2< and <3 but its a 90°
so....<2 = 90° - 36°
= 54
u should get the <4 too....
hope u get it
please mark me brilliant
what is the equation of the new line?
Answer:
y = 2/3x - 3
Step-by-step explanation:
Given equation :-
y = 2/3x + 2Transformations :-
Shifted down 5 units⇒ Slope remains same, y-intercept decreases by 5Solving :-
New equation ⇒ y = 2/3x + 2 - 5y = 2/3x - 3The graph shows the distance cars A and B travel.
Which statement is true about the unit rates shown in the graph?
A. The unit rate for car A is greater because the slope is greater than the slope for car B.
B. The unit rate for car B is greater because the slope is less than the slope for car A.
C. The unit rate for car A is greater because the slope is less than the slope for car B.
D. The unit rate for car B is greater because the slope is greater than the slope for car A.
Answer:
(a) The unit rate for car B is greater because the slope is greater than the slope for car A.
Step-by-step explanation:
We have been given a graph that represents the distance cars A and B travel. We are asked to choose the correct option about our given graphs.
Since slope represents the change in y-value with respect to change in per unit x value, so slope is also unit rate of the graph.
Let us find the slope of car A using points (8,5) and (0,0).
Let us find the slope of car B using points (5,8) and (0,0).
We can see that slope of car B is greater than slope of car A, therefore, option A is the correct choice.
Step-by-step explanation:
what is the missing value of 8/40 = 12/n
Answer:
The answer is 60!
The diagram shows a tetrahedron.
AD is perpendicular to both AB and AC.
AB = 10 cm.
AC = 8 cm.
AD = 5 cm.
Angle BAC = 90°
Calculate the size of angle BDC.
Give your answer correct to 1 decimal place.
=================================================
Work Shown:
For now focus on triangle ABC. Since this is a right triangle, we can use the pythagorean theorem to find the hypotenuse BC.
a^2 + b^2 = c^2
(AC)^2 + (AB)^2 = (BC)^2
8^2 + 10^2 = (BC)^2
(BC)^2 = 164
BC = sqrt(164)
BC = 12.806248 approximately
-------------
Move onto triangle ABD. Find the missing side BD through the pythagorean theorem
a^2 + b^2 = c^2
(AD)^2 + (AB)^2 = (BD)^2
5^2 + 10^2 = (BD)^2
125 = (BD)^2
(BD)^2 = 125
BD = sqrt(125)
BD = 11.1803399 which is approximate
---------------
Move onto triangle ADC. We'll use the pythagorean theorem again
a^2 + b^2 = c^2
(AC)^2 + (AD)^2 = (CD)^2
8^2 + 5^2 = (CD)^2
89 = (CD)^2
(CD)^2 = 89
CD = sqrt(89)
CD = 9.433981 also approximate
---------------
Focus on triangle BCD. We have the following side lengths
BC = 12.806248 BD = 11.1803399CD = 9.433981Let
side d be opposite angle D, so d = BC = 12.806248 side b be opposite angle B, so b = CD = 9.433981side c be opposite angle C, so c = BD = 11.1803399Note the use of uppercase letters for angles and lowercase letters for side lengths.
We can then use the law of cosines to find the angle we're after
d^2 = b^2 + c^2 - 2*b*c*cos(D)
12.806248^2=9.433981^2+11.1803399^2-2*9.433981*11.1803399*cos(D)
163.999987837504=213.999997787893-210.950228380284*cos(D)
-210.950228380284*cos(D) = -50.000009950389
cos(D) = (-50.000009950389)/(-210.950228380284)
cos(D) = 0.237022781792173
cos(D) = arccos(0.237022781792173)
D = 76.2891111084541
D = 76.3
The size of the angle ∠BDC of the tetrahedron can be determined by
cosine rule.
The size of angle ∠BDC is approximately 71.1°
Reasons:
A tetrahedron is a pyramid with triangular faces.
By Pythagoras's theorem, we have;
[tex]\overline{DC}[/tex]² = [tex]\mathbf{\overline{AD}}[/tex]² + [tex]\mathbf{\overline{AC}}[/tex]²
∴ [tex]\overline{DC}[/tex]² = 8² + 5² = 89
[tex]\overline{DC}[/tex]² = 89
[tex]\overline{BC}[/tex]² = [tex]\overline{AB}[/tex]² + [tex]\overline{AC}[/tex]²
∴ [tex]\overline{BC}[/tex]² = 10² + 8² = 164
[tex]\overline{BC}[/tex]² = 164
[tex]\overline{DB}[/tex]² = [tex]\mathbf{\overline{AD}}[/tex]² + [tex]\mathbf{\overline{AB}}[/tex]²
[tex]\overline{DB}[/tex]² = 5² + 10² = 150
[tex]\overline{DB}[/tex]² = 150
By cosine rule, we have;
[tex]\overline{BC}[/tex]² = [tex]\overline{DB}[/tex]² + [tex]\overline{DC}[/tex]² - 2 × [tex]\mathbf{\overline{DB}}[/tex] × [tex]\mathbf{\overline{DC}}[/tex] × cos(∠BDC)
Therefore;
164 = 150 + 89 - 2 × √(150) × √(89) × cos(∠BDC)
2 × √(150) × √(89) × cos(∠BDC) = 150 + 89 - 164 = 75
[tex]cos( \angle BDC) = \mathbf{\dfrac{75}{2 \times \sqrt{150} \times \sqrt{89} }}[/tex]
[tex]\angle BDC = arccos \left(\dfrac{75}{2 \times \sqrt{150} \times \sqrt{89} } \right) \approx \mathbf{71.1 ^{\circ}}[/tex]
∠BDC ≈ 71.1°
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Jace walked a total distance of StartFraction 5 Over 6 EndFraction of a mile to school this week. If he walked the same distance each of the 5 days, how far did he walk each day?
He walks 5/6 of a mile each day.
Multiply the distance each day by the number of days:
5/6 x 5
When multiplying a fraction by a whole number, multiply the numerator ( top number) by the whole number and leave the denominator ( bottom number as is)
5/6 x 5 = (5 x5)/6 = 25/6 now rewrite as a proper fraction:
25/6 = 4 1/6 total miles.
Answer:
4 1/6 miles over the course of 5 days
Step-by-step explanation:
The radius of a circular pond is increasing at a constant rate, which can be modeled by the function , where t is time in months. The area of the pond is modeled by the function . The area of the pond with respect to time can be modeled by the composition . Which function represents the area with respect to time? A. B. C. D.
Answer:
B. A(r(t)) = 25πt²
Step-by-step explanation:
Find the completed question below
The radius of a circular pond is increasing at a constant rate, which can be modeled by the function r(t) = 5t where t is time in months. The area of the pond is modeled by the function A(r) = πr². The area of the pond with respect to time can be modeled by the composition . Which function represents the area with respect to time? A. B. C. D.
Given
A(t) = πr²
r(t) = 5t
We are to evaluate the composite expression A(r(t))
A(r(t)) = A(5t)
To get A(5t), we will replace r in A(t) with 5t and simplify as shown
A(5t) = π(5t)²
A(5t) = π(25t²)
A(5t) = 25πt²
A(r(t)) = 25πt²
Hence the composite expression A(r(t)) is 25πt²
Option B is correct.
Answer:
Step-by-step explanation:
B . Correct
5. Find three solutions of the equation (1 point)
y = 2x - 6
(-2.-10). (1.-4). (2. -1)
(-2,-10), (1.-4), (0.6)
(0.–6). (3.-2) (-2,-10)
(1.-4), (0.-6). (-1,-9)
The answer might be c. not 100% sure sorry
PLEASE HELP ill Mark BRAINLIEST 31 points too
Answer:(-1,7)
Step-by-step explanation:
What is the area of this figure?
Drag and drop the appropriate number into the box.
Please help!
Thank you! <3
Answer:
441
Step-by-step explanation:
I think
y =400(.99)x growth or delay?
Answer:
Delay
Step-by-step explanation:
Because you are multiply x into 0.99, every time the multiplication takes place it will only become 99% of the value of the product of x and 400.
find measure of w in this trapezoid *please help*
Answer:
34°
Step-by-step explanation:
sum interior measure = (n-1)*180 ; n is the number of sides
of the polygon
(n-1)*180
(4-2)*180
2*180
360° ( sum interior measure )
The angles of the quadrilateral are ( 90 , 90 , w , 146 )
90+90+146+w = 360
326+w = 360
w = 360-326
w = 34°
Hope you get benefit from it
i need for homework please answer
Answer:
well, they all give you answers as fractions,
A.=1/9
B.=1/64
C.=1/64
Step-by-step explanation:
Use the figure to complete a-d
For what value of k does the equation have no solution? kx - 4 = 5x + 8
Answer:
Your answer is: k = 5+12/x
Isolate the variable by dividing each side by factors that don't contain the variable.
Step-by-step explanation:
Hope this helped : )
3. Which is NOT a way to write a ratio?
Answer:
Lowest term
Step-by-step explanation:
you can write a ratio using a fraction form, a colon form, and a word form. The lowest term is just a part of an answer.
How to find the angle measure x in the figures
Answer:
subtract 180 from the other two angles
Step-by-step explanation:
triangle involves 3 angles with x's in the equation, set the 3 angles = to 180 and solve
2 320 is invested for two years
at 14% p.a simple interest
At 12% p.a compound interest
which is a better investment and by how much
Answer:
which is a better investment and by how muchIt's 14% p.a simple interest
Step-by-step explanation:
Simple interst:
Answer:
I = $ 649.60
Equation:
I = Prt
Calculation:
First, converting R percent to r a decimal
r = R/100 = 14%/100 = 0.14 per year,
then, solving our equation
I = 2320 × 0.14 × 2 = 649.6
I = $ 649.60
The simple interest accumulated
on a principal of $ 2,320.00
at a rate of 14% per year
for 2 years is $ 649.60.
Compound interest
Answer:
A = $2,945.78
A = P + I where
P (principal) = $2,320.00
I (interest) = $625.78
Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 12/100
r = 0.12 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 2,320.00(1 + 0.12/12)(12)(2)
A = 2,320.00(1 + 0.01)(24)
A = $2,945.78
Summary:
(20 points) It has been suggested that the highest priority of retirees is travel. Thus, a study was conducted to investigate the differences in the
length of stay of a trip for pre- and post-retirees. A sample of 697 travelers were asked how long they stayed on a typical trip. The observed results
of the study are found below.
The expected frequencies from the data conducted to investigate the differences in the length of stay of a trip will be 221.7097, 72.471, 49.3881, and 25.7677.
How to calculate the expected frequencies?From the complete question, the expected frequencies from the data about the trip will be calculated thus:
E(240) = (379 × 413) ÷ 706
=221.7097
E(83) =(379 × 153) ÷ 706
=72.471
E(40) = (379 × 92) ÷ 706
=49.3881
E(16) =(379 × 48) ÷ 706
=25.7677
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If a book rests on a flat table in what direction does the normal force from the table act on the book?
Answer:
The normal force is the force that a surface makes on an object that lies on that surface.
As the book rest flat in the table, the force acting on the book will be the gravitational force. This force pulls down the book against the table, then the normal force will be opposite to this, then the direction of this force is upwards. Being more exact, the normal force always acts on the normal direction to a given surface, to find the normal of a surface, you need to find the plane of the surface, then any perpendicular line to that surface will be "normal" to the surface (and the normal direction points away from the surface) then if the book is resting on top of the table, the direction of the normal will be upwards..
Then the force that acts on the book is normal to the surface of the table,
Hello people ~
factorise: p² - 13p - 30
Answer:
[tex] {p}^{2} - 13p - 30 \\ \\ {p}^{2} - 15p - 2p - 30 \\ \\ p(p - 15) + 2(p - 15) \\ \\ (p + 2)(p - 15)[/tex]
# Jerry Don is here#
Answer:
[tex]\displaystyle [p + 2][p - 15][/tex]
Explanation:
Find two quantities that when differed to 13, they also multiply to 30. Those will be 2 and 15. The TINIER quantity gets the plus sign because the B-value is −13, therefore 15 gets the minus sign, leaving 2 with the plus sign.
I am joyous to assist you at any time.
HELP HELP HELPPPP question is in the Image pls help as soon as you can
Step-by-step explanation:
the answer is the last one, because if you plug in (5, -6) to both equations you would get equal answer.
Answer:
D
Step-by-step explanation:
5=x and -6=y so 5+-6 or 5-6=-1 so it makes the first equation true. Then plug it in to the second equation. (3)(5)--6 or (3)(5)+6 which = 15+6. 15+6=21. So both are true. Btw Im new to this hope this helps!