Answer:
Let the number of courses that are worth 3 credits each be x and those worth 4 credits be y. With the given information, you can write the following equations:
x + y = 48
3x + 4y = 155
You can solve the above equations by method of elimination/substitution
x + y = 48 ⇒ x = 48 - y (Now, substitution this equation into 3x + 4y = 155)
3(48 - y) + 4y = 155
144 -3y + 4y = 155
y + 144 = 155
y = 11
Now plug this solution back into x = 48 - y
x = 48 - 11 = 37
Check work (by plugging the solutions back into the 3x + 4y and see if it's equal to 155):
3(37) + 4(11) = 155
Answer: There are 37 of the 3-credit course and 11 of the 4-credit course
The least-squares regression equation
y = 8.5 + 69.5x can be used to predict the monthly cost for cell phone service with x phone lines. The list below shows the number of phone lines and the actual cost.
(1, $90)
(2, $150)
(3, $200)
(4, $295)
(5, $350)
Calculate the residuals for 2 and 5 phone lines, to the nearest cent.
The residual for 2 phone lines is $___
The residual for 5 phone lines is $___
Answer:
First one: 2.5
Second: -6
8.5+69.5(5) = 147.5
150 - 147.5 = 2.5
8.5 + 69.5(5) = 356
350 - 356 = -6
ED2021
The residual for 2 phone lines is $2.5.
The residual for 5 phone lines is -$6.
What is the residual in a least-square regression equation?
The residual is the vertical distance separating the observed point from your expected y-value, or more simply put, it is the difference between the actual y and the predicted y.
How to solve the question?In the question, we are asked to find the residual for 2 and 5 lines using the least-squares regression equation y = 8.5 + 69.5x and the actual costs given to us.
We know that the residual is the vertical distance separating the observed point from your expected y-value, or more simply put, it is the difference between the actual y and the predicted y.
Thus for 2 phone lines:-
Actual Cost = $150.
Predicted Cost, y = 8.5 + 69.5*2 = 147.5.
Residual = Actual Cost - Predicted Cost = 150 - 147.5 = $2.5.
Thus, the residual for 2 phone lines is $2.5.
Thus for 5 phone lines:-
Actual Cost = $350.
Predicted Cost, y = 8.5 + 69.5*2 = 356.
Residual = Actual Cost - Predicted Cost = 350 - 356 = -$6.
Thus, the residual for 2 phone lines is -$6.
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Given the following matrices, what 3 elements make up the first column of the product matrix DA?
We have to figure out what the product of DA is,
[tex]\begin{bmatrix}-1&2&3\\8&-4&0\\6&7&1\\ \end{bmatrix}\begin{bmatrix}1\\3\\5\\ \end{bmatrix}=\begin{bmatrix}a\\b\\c\\ \end{bmatrix}[/tex]
We know that,
[tex]\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\\\end{bmatrix}\begin{bmatrix}x\\y\\z\\\end{bmatrix}=\begin{bmatrix}ax+by+cz\\dx+ey+fz\\gx+hy+iz\\\end{bmatrix}[/tex]
So,
[tex]a=-1\cdot1+2\cdot3+3\cdot5=-1+6+15=20[/tex]
[tex]b=8\cdot1+(-4)\cdot3+0\cdot5=8-12=-4[/tex]
[tex]c=6\cdot1+7\cdot3+1\cdot5=6+21+5=32[/tex]
So the solution is,
[tex]a,b,c=\boxed{20,-4,32}[/tex]
Hope this helps :)
Which function has a domain and range that includes all real values?
Answer:
the third one
the line extends in both ways forever
write your answer in simplest radical form
Answer:
[tex]s=6\sqrt{3}[/tex]
Step-by-step explanation:
In any 30-60-90 triangles, the sides are in ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the hypotenuse of the triangle.
In the given diagram, the hypotenuse is marked as 12 miles. Therefore, the side opposite to the 30 degree angle must be [tex]12 \div 2=6[/tex] miles. The final leg, [tex]s[/tex], must then represent the [tex]x\sqrt{3}[/tex] part of our ratio, hence [tex]\implies \boxed{6\sqrt{3}}[/tex]
The sum of the two numbers is 66. The larger number is 10 more than the smaller number. What are the numbers?
Answer:
28 and 38
Step-by-step explanation:
a+b = 66
a + 10 = b
using substitution, a + (a+10) = 66
2a = 56
a = 28
28 + 10 = 38
b = 38
Which of the following graphs represents a one-to-one function? On a coordinate plane, a function has two curves connected to a straight line. The first curve has a maximum of (negative 6, 4) and a minimum of (negative 4.5, negative 1). The second curve has a maximum of (negative 3.5, 2) and a minimum of (negative 2.5, 0.5). The straight line has a positive slope and starts at (negative 2, 1) and goes through (1, 2). On a coordinate plane, a circle intersects the x=axis at (negative 2, 0) and (2, 0) and intercepts the y-axis at (0, 4) and (0, negative 4). On a coordinate plane, a v-shaped graph is facing up. The vertex is at (0,0) and the function goes through (negative 4, 4) and (4, 4). A coordinate plane has 7 points. The points are (negative 4, 1), (negative 3, 4), (negative 1, 3), (1, negative 3), (3, negative 4), (4, negative 2), (5, 3). Mark this and return
Answer:
d. this graph
Step-by-step explanation:
HELPPP!!!
find the area of a triangle with a height of 9cm and a base of 5 cm
Answer:
A = 22.5 cm^2
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh where b is the base and h is the height
A = 1/2(5)(9)
A = 45/2
A = 22.5 cm^2
[tex]\begin{gathered} {\underline{\boxed{ \rm {\red{Area \: \: of \: \: triangle \: = \: \frac{1}{2} \: \times \: base \: \times \: height}}}}}\end{gathered}[/tex]
Base of triangle = 5 cm.Height of triangle is 9 cm.Solution[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \frac{1}{2} \: \times \: 5 \: cm \: \times \: 9 \: cm[/tex]
[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \frac{1}{2} \: \times \: 45 \: cm[/tex]
[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \frac{45 \: {cm}^{2} }{2} \: \\ [/tex]
[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \cancel\frac{45}{2} \: \: ^{22.5 \: {cm}^{2} } \: \\ [/tex]
[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: 22.5 \: {cm}^{2} [/tex]
Hence , the area of triangle is 22.5 cm²
What is the remainder when () = 3 − 11 − 10 is divided by x+3
Answer:
-18/x+3
Step-by-step explanation:
what value of x is in the solution set of 8x-6>12+2x
Answer:
x>3
Step-by-step explanation:
8x - 2x > 12+ 6
-> 6x > 18
-> x > 3
[tex] \: \: \: \huge \rm{answer: \blue{ \boxed{ \rm{ \pink{x > 3}}}}}[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
[tex] \huge \blue{ \boxed{ \pink{\boxed{ \rm{ \blue{armed }\: account}}}}}[/tex]
➙[tex] \huge \rm8x-6>12+2x \\ \rm \huge8x-2x>12+6 \\ \huge\rm6x>18 \\ \huge \boxed{\rm{x>3}}[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖
I hope you understood!✏
➖➖➖➖➖➖➖➖➖➖➖➖➖➖
Step-by-step explanation:
[tex] \huge \boxed{ \boxed{\rm{Hope \: this \: helps}}}[/tex]
How many degrees must the flyswatter pass through before it is horizontal?
Answer:
90°
Step-by-step explanation:
assuming it's upright and you swat it down it will go down by 90°
Type an equation for the
following pattern.
x
1 -2
2
4
3
-6
y=[? ]x+[ ]
4
-8
S
- 10
Answer:
y=-2x
Step-by-step explanation:
first find the slope: (-2-(-4))/(1-2)=2/-1=-2 so m=-2
now we have y=-2x+b, to find b we plug in any of the points
-2=-2(1)+b-2=-2+b b=0so the equation is y=-2x
Helppppp plzzzzzzz!!!!!!!!!!! 15+ PTS and brainliest!!!!!!!!
Write the equation of the line with slope of 0, and y-intercept of 9.
Answer:
y=0x+9. Hope this helped.
Step-by-step explanation:
slope intercept form: y=mx+b
m represents slope
b represents the y intercept. Please give me the brainliest:)
2
7) through: (-3,0), slope
3
Answer:
Step-by-step explanation:
Point-slope equation for line of slope m that passes through (x₀, y₀):
y-y₀ = m(x-x₀)
Slope =3 and (x₀, y₀)=(-3,0)
y = 3(x+3)
y = 3x+ 9
:::::
Slope-intercept equation for line of slope m and y-intercept b:
y = mx+b
m=1 and b= -4:
y = x-4
PLEASE HELP!!!
Evaluate each expression.
(252) =
Answer:
1/5
Step-by-step explanation:
substitute for A,P and T in the fomula A=P (1+r)^t,give that A=1 000 000,P=10 000 and T=2,and express as a quadratic equation
A = 10,00,000
P = 10,000
T = 2
1000000 = 10000(1+r/100)^2
1000000 = 10000((100 + r)/100)^2
1000000 = 10000× 100 + r/100 × 100 + r/100
1000000 = 10000 + r^2
1000000 - 10000 = r^2
990000 = r^2
√99000 = r
Quadratic Equation
10000(1+r/100)^2
A kite is a ........... quadrilateral
Answer:
yes
Step-by-step explanation:
The complete sentence is,
A kite is a convex quadrilateral.
We have to given that,
To find a kite is which type of a quadrilateral.
We know that,
A quadrilateral known as a kite has four sides that may be divided into two pairs of neighboring, equal-length sides.
The two sets of equal-length sides of a parallelogram, however, are opposite one another as opposed to being contiguous.
Hence, The complete sentence is,
A kite is a convex quadrilateral.
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Please help explanation if possible
Answer:
N=18
Step-by-step explanation:
Hope it will help you
If it does pls give me Brainlest
Have a nice day
Answer:
18
Step-by-step explanation:
use the concept of similarity and enlargement.
[tex] \frac{15}{n} = \frac{5}{6 } [/tex]
[tex]n = \frac{15 \times 6}{5} [/tex]
[tex]n = 18[/tex]
Value of [(3/2)^(-2)] is *
Answer:
[tex] { (\frac{3}{2} )}^{ - 2} \\ = { (\frac{2}{3}) }^{2} \\ = \frac{4}{9} \\ thank \: you[/tex]
Calculate a high estimate for each. Show your work?81×37
Step-by-step explanation:
2997
81
×
37
=2997
it just a simple calculation just multiply the numbers
Which of the following rational functions is graphed below?
o
A. F(x) = 1/2x
B. AX) = 1/x-2
C. F(x) = 1/x+2
Answer:
Option B.
Step-by-step explanation:
We can see that we have an asymptote at x = 2
Remember that in a rational function, the asymptote is at the x-value such that the denominator is equal to zero.
So, the denominator is something like:
(x + a)
we have that the denominator is zero when x = 2
Then:
(2 + a) = 0
solving that for a, we get:
a = -2
Then the denominator of the rational function is:
(x - 2)
For the given options, the only one with this denominator is option B, then the correct option is B.
Answer:
B. f(x) = 1/x-2
Step-by-step explanation:
Math is ez bro.
find the measure of x
Answer:
[tex]B)\ x=43[/tex]
Step-by-step explanation:
One is given a circle with many secants within the circle. Please note that a secant refers to any line in a circle that intersects the circle at two points. A diameter is the largest secant in the circle, it passes through the circle's midpoint. One property of a diameter is, if a triangle inscribed in a circle has a side that is a diameter of a circle, then the triangle is a right triangle. One can apply this to the given triangle by stating the following:
[tex]x+47+90=180[/tex]
Simplify,
[tex]x+47+90=180[/tex]
[tex]x+137=180[/tex]
Inverse operations,
[tex]x+137=180[/tex]
[tex]x=43[/tex]
the mode of 3,5,1,2,4,6,0,2,2,3 is
giving out brainliest
find lub and glb of the following set E={0.2, 0.23, 0.234, 0.2343, 0.23434, 0.234343,.....}
The lub is 0.23[tex]\mathbf{\overline{43}}[/tex], while the glb is 0.2
The given set is presented as follows;
E = {0.2, 0.23, 0.234, 0.2343, 0.23434, 0.234343,...}
The least upper bound, lub, of a set, E, is known as the supremum of the set which is the number B such that all x ∈ E are of the value x ≤ B, while there all y ∈ E has a x ∈ E such that t < x
Therefore;
The supremum, lub of the given set is 0.23[tex]\overline{43}[/tex]
The greatest lower bound, glb, b, also known as the infimum, is defined as follows;
b is the greatest lower bound if for all x ∈ E then x ≥ b
Given that b < t, then where x ∈ E, there exist a x < t
The glb of the given set is 0.2
Learn more about lub, supremum, glb, infimum, here;
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The question is in the screenshot
Answer:
AC is about 4.29
Step-by-step explanation:
we need to use simple trigonometry for this problem
the tangent of an angle is the ratio between the opposite side and the adjacent side
so the tangent of the angle 35º is BC / AC
tan(35) is about 0.7
this means that BC / AC = 0.7
we know BC is 3
so 3 / AC = 0.7
3 = 0.7(AC)
AC is about 4.29
Given two dependent random samples with the following results: Population 1 30 35 23 22 28 39 21 Population 2 45 49 15 34 20 49 36 Use this data to find the 90% confidence interval for the true difference between the population means. Assume that both populations are normally distributed. Step 1 of 4: Find the point estimate for the population mean of the paired differences. Let x1 be the value from Population 1 and x2 be the value from Population 2 and use the formula d=x2−x1 to calculate the paired differences. Round your answer to one decimal place.
Answer:
(-14.8504 ; 0.5644)
Step-by-step explanation:
Given the data:
Population 1 : 30 35 23 22 28 39 21
Population 2: 45 49 15 34 20 49 36
The difference, d = population 1 - population 2
d = -15, -14, 8, -12, 8, -10, -15
The confidence interval, C. I ;
C.I = dbar ± tα/2 * Sd/√n
n = 7
dbar = Σd/ n = - 7.143
Sd = standard deviation of d = 10.495 (using calculator)
tα/2 ; df = 7 - 1 = 6
t(0.10/2,6) = 1.943
Hence,
C.I = - 7.143 ± 1.943 * (10.495/√7)
C.I = - 7.143 ± 7.7074
(-14.8504 ; 0.5644)
A 10-ft ladder, whose base is sitting on level ground, is leaning at an angle against a vertical wall when its base starts to slide away from the vertical wall. When the base of the ladder is 6 ft away from the bottom of the vertical wall, the base is sliding away at a rate of 4 ft/sec. At what rate is the vertical distance from the top of the ladder to the ground changing at this moment?
Answer:
2.5/ft per sec
Step-by-step explanation:
its vertica.
The height of the ladder is decreasing at a rate of 24 ft/sec.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
Let's denote the distance between the base of the ladder and the wall by x.
The length of the ladder = L.
Now,
L = 10 ft
dx/dt = 4 ft/sec
x = 6 ft.
The rate of change of the height of the ladder with respect to time.
Using the Pythagorean theorem, we have:
L² = x² + y²
Differentiating both sides with respect to time t, we get:
2L (dL/dt) = 2x(dx/dt) + 2y(dy/dt)
Substituting L = 10 ft, x = 6 ft, and dx/dt = 4 ft/sec.
20(dL/dt) = 12(4) + 2y(dy/dt)
Simplifying and solving for dy/dt.
dy/dt = (20/2y)(dL/dt) - 24
Now,
The height of the ladder.
Using the Pythagorean theorem again, we have:
y² = L² - x²
= 100 - 36
= 64
y = 8
Now,
Substituting y = 8 ft, dL/dt = 0
(since the length of the ladder is constant), and dx/dt = 4 ft/sec.
dy/dt
= (20/2(8))(0) - 24
= -24 ft/sec
Therefore,
The height of the ladder is decreasing at a rate of 24 ft/sec.
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The radius of a circle is increasing at the rate of 0.1 cm/sec. At what rate is the area
increasing at the instance when r=5cm?
Answer:
3.1416
Step-by-step explanation:
A=pi*r^2, differentiate with respect to t both sides
dA/dt=2*pi*r*dr/dt
dA/dt=2*pi*5*(0.1)
dA/dt=pi=3.1416 cm^2/sec
Step-by-step explanation:
since the user is listed as beginner, I was wondering, if (while correct) the answer should be based on differentiation (rather advanced topic).
I thought originally this would be about sequences.
and I wondered about the start value.
in any case, here a different view.
the area of a circle is
Ac old = pi × r²
now, r is increasing by 0.1
Ac new = pi×(r+0.1)² = pi×(r² + 0.2r + 0.01) =
= pi×r² + pi×0.2r + pi×0.01 =
= Ac old + pi×0.2r + pi×0.01
so, the increase of the area is
pi×0.2r + pi×0.01
for r=5
pi×0.2×5 + pi×0.01
pi×1 + pi×0.01 = pi + p×0.01 = pi×(1 + 0.01) =
= pi×(1 + (radius change)²)
now, it depends on what your teacher wants to see here.
a "digital stair case" 0.1 by 0.1 increase/sequence approach ?
in this case you might also want to calculate the above with r=4.9 (as only with the last 0.1 step r reaches 5).
and either the r=4.9 (result a tiny bit less than pi) or r=5 (result a tiny bit larger than pi) is correct, of simply the value in the middle (practically pi).
or it was meant to be a continuous increase (not step by step).
in which case we need then to calculate the limit with "radius change" going to 0. which delivers pi as rate result (as with the differentiation).
Nhà trường muốn đánh giá tỉ lệ chăm học của sinh viên (trong một tuần). Khảo sát 236 sinh viên thì thấy có 32 sinh viên chăm học. Hãy ước lượng khoảng đối xứng cho tỉ lệ sinh viên chăm học của trường với độ tin cậy 95%
Answer:
can't understand the language
Luisa and Rachelle are competing for employee of the month. It is the last week, and the employee who processes the most client accounts will win. Luisa processed 15 accounts Monday, 22 accounts Tuesday, and 17 accounts Wednesday. Rachelle processed 24 accounts Monday, 18 accounts Tuesday, and 11 accounts Wednesday. Who has processed the most accounts this week, and by how many
Answer:
Luisa processed the most accounts this week, by 1.
Step-by-step explanation:
Luisa:
15 on Monday, 22 on Tuesday and 17 on Wednesday.
So a total of 15 + 22 + 17 = 54.
Rachelle:
24 on Monday, 18 on Tuesday, 11 on Wednesday.
So a total of 24 + 18 + 11 = 53.
Who has processed the most accounts this week, and by how many?
54 - 53 = 1, so Luisa processed the most accounts this week, by 1.
Use the graph to complete the statement. O is the origin. r(180°,O) ο Ry−axis : (2,5)
A. ( 2, 5)
B. (2, -5)
C. (-2, -5)
D. (-2, 5)
9514 1404 393
Answer:
B. (2, -5)
Step-by-step explanation:
Reflection across the y-axis is the transformation ...
(x, y) ⇒ (-x, y)
Rotation 180° about the origin is the transformation ...
(x, y) ⇒ (-x, -y)
Applying the rotation after the reflection, we get ...
(x, y) ⇒ (x, -y)
(2, 5) ⇒ (2, -5)
_____
Additional comment
For these transformations, the order of application does not matter. Either way, the net result is a reflection across the x-axis.
Answer:
(2,-5)
Step-by-step explanation:
