Since the situation can be since as an arithmetic sequence, her salary after 3 years is $73,000. After t years, her salary is a function of t, that is a(t) = 64000 + 3000 t
The given situation can be seen as an arithmetic sequence. The nth term of an arithmetic sequence is given by the formula:
a(n) = a(1) + (n - 1) . d
Where:
a(1) = the first term
d = the common difference.
The problem can be translated into an arithmetic sequence with:
a(1) = $67000
d = $3000
Kylie's salary after 3 years is a(3),
a(3) = a(1) + (3 - 1) . d
a(3) = Kylie's salary + 2 . 3000 = 73000
Hence, after 3 years, Kylie's salary is $73,000
Her salary after t years, means n = t. Therefore,
a(t) = a(1) + (t - 1) . d
a(t) = 67000 + (t -1) . 3000
a(t) = 64000 + 3000 t
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find the equation of the line parallel to y=3x+4 and that passes through the point (-5,4)
Answer:
y = 3x + 19
Step-by-step explanation:
Equation of line in slope y-intercept form: y = mx +bHere m is the slope and b is the y-intercept.
y = 3x + 4
m = 3
Parallel lines have same slope.
m = 3
y = 3x + b
Substitute (-5,4) in the above equation.
4 = 3*(-5) + b
4 = -15 + b
4 + 15 = b
b = 19
Equation of the line: y = 3x + 19
Answer: y = 3x +19
Step-by-step explanation:
-Parallel lines have the same gradient
y = 3x + c
rearrange to give c= y - 3x
substitute x = -5 and y = 4
c = 3 - (3x-5)
c= 19
so the equation is y = 3x + 19
what is the square of 77.5?
To construct the angle bisector of ∠ABC, first set the point of the compass on and draw an arc through and
The construction of the angle bisector of [tex] \angle ABC[/tex], gives the completed statement as follows;
Set the point of the compass on B and draw an arc through arms AB and BCWhat is an angle bisector?An angle bisector is the ray or line, dividing an angle into two congruent angles.
The steps required to construct the angle bisector of [tex] \angle ABC[/tex] is presented as follows;
Place the compass at point B which is the vertex of [tex] \angle ABC[/tex] and draw arcs to intersect the arms or segments BA and BCLabel the point of intersection of the arcs and the arms of the angle [tex] \angle ABC[/tex] as points D and EPlace the compass at point D and draw an arc on the inside of [tex] \angle ABC[/tex] and on the side further from point B than D Repeat the above process by placing the compass at point E and drawing an arc to intersect the arc drawn from point D at point FJoin the points B and F with the straightedge to complete the construction of the angle bisector of [tex] \angle ABC[/tex], which is segment BFThe complete statement is therefore;
To construct the angle bisector of.[tex] \angle ABC [/tex], first set the point of the compass on B and draw an arc through BA and BC
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if a baseball player has a batting average of 0.330, what is the probability that the player will get the following number of hits in the next four times at bat?
The player has a 0.293 percent probability of getting the subsequent number of hits in the subsequent four at-bats.
What does probability mean in math?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.
In light of the information provided,
designate X as the random variable indicating the player's hit total during his subsequent four at-bats.
Assume that the player hits or misses on each of the following four at-bats in a random order. Consider it a success if the player gets a hit as well.
The probability of "success" is because of the batting average, which is 0.330.
In this case, x can be thought of as the overall success rate across the four at-bats. Inferring that X has a binomial distribution with p=0.330 as its parameters
n=4 p=0.330
Since p denotes the probability of success, the probability of failure is
q=1-0.330
=670
The probability mass function of x here is
f(x)={(4 0)*(0.330)ˣ (0.670)⁽⁴⁻ˣ⁾
The probability that the player will get exactly 2 hits, that is, is calculated below:
P(2)=F(2)={(4+2)*(0.330)² (0.670)²
=6[0.04888]
=0.29328
Thus, the probability that the player will get exactly 2 hits is 0.239.
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Simplify:
5/8(-8j+24)
Answer: -5j+15
step by step equation
What is the volume of a cube with edge length 13 cm in cubes
6. The price x of a new car minus à 25% down payment.
The expression that shows the price x of a new car minus à 25% down payment is x - 0.25 = 0.75x
How to illustrate the information?Based on the information given, it should be noted that the information is to simply illustrate find the expression that shows the price x of a new car minus a 25% down payment.
This will be illustrated as:
= x - (25% × x)
= x - 0.25x
= 0.75x
Therefore, the expression is 0.75x.
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Anna is following this recipe to make biscuits.
Anna uses 120 g of chocolate.
How many grams of margarine will she need?
Recipe: Makes 24 biscuits
80 g sugar
120 ml syrup
200 g oats
120 g margarine
40 g chocolate
Anna uses 120 g of chocolate and 360 grams of margarine to needed to bake biscuits.
We have data as follows; To make 24 biscuits Anna uses following proportion of Ingredients;
80 g sugar
120 ml syrup
200 g oats
120 g margarine
40 g chocolate
Now We can analysis that anna uses 40 g chocolate to make 24 biscuits
So for 120 g of chocolate Anna can bake [tex] \frac{24(120)}{40} [/tex]
= 24 (3)
= 72 biscuits
∴ Anna can bake 72 biscuits if she uses 120 g of chocolate.
We want to find how many grams of margarine will she need to make 72 biscuits and this can be done as follows;
Ingredients for 24 biscuits require 120 g margarine
∴ For 72 biscuits anna require [tex] \frac{72(120)}{24} [/tex] g of margarine
= 3 (120)
= 360 g of margarine.
Hence 360 grams of margarine anna needed.
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Is the function represented by the table non-linear?
X
6
7
8
9
y
4
2
0
-2
OYes, because it has a constant rate of change.
O Yes, because it does not have a constant rate of change.
O No, because it has a constant rate of change.
O No, because it does not have a constant rate of change.
pls help me on problem 45 will give u brainliest (7th grade math)
WILL GIVE BRAINLIEST
The average daily profit of an electronics store is $31,435. The company estimates that 15% is lost each day to returns, with a margin of error of ±4%. What is the maximum the company can expect for returned items?
$3457.85
$4621.13
$5972.65
$6638.22
The maximum that the company can expect for returned items is C. $5972.65
How to calculate the value?From the information, the average daily profit of an electronics store is $31,435 and the company estimates that 15% is lost each day to returns, with a margin of error of ±4%.
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and research results using the margin of error.
The maximum the company can expect for returned items will be:
= (15% + 4%) × Profit
= 19% × $31,435
= 0.19 × $31,435
= $5972.65
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Geometry
In the diagram, ZJKM is a straight angle
Intro
K
M
Which statements about the diagram are true? Check
all that apply.
Dk is an angle bisector.
OLKQ is bisected.
Dm/JKL=45"
Om MKQ+m/PKQ = m/PKM
OPK is an angle bisector.
OZJKL
The statements that are true are:
3) m∠JKL = 45°
4) m∠MKQ + m∠PKQ = m∠PKM
5) line PK is an angle bisector
1) This statement says that KQ is an angle bisector. This is false because the line KQ does not pass through the diagonal vertex of the right angled symbol at point K.
2) Second statement says that ∠LKQ is bisected. This statement is false because PK is just a perpendicular line to JKM that divides it into 2 equal parts and not a bisector of ∠LKQ
3) The third statement states that m∠JKL = 45°. This statement is true because from the image it is clear that the line KL divides m∠PKJ into two equal parts.
4) Fourth statement says that m∠MKQ + m∠PKQ = m∠PKM. This statement is true. Now, although KQ doesn't bisect m∠PKM into 2 equal parts, nevertheless it divides it into 2 angles namely m∠MKQ and m∠PKQ. This means the sum of m∠MKQ + m∠PKQ must yield m∠PKM.
5) The fifth statement says that the line PK is an angle bisector. This statement is true because JKM is a straight angle. Thus as PK is perpendicular to it, it has bisected it into two equal parts.
6) The fifth statement says that ∠JKL ≅ ∠QKM. This statement is false because ∠JKL is a bisected angle which is 45° whereas, ∠QKM is not a bisected angle and thus not equal to 45°.
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Calculate the measure of ∠1 using the Exterior Angle Theorem.
Triangle PUB is divided into 2 triangles that is ΔPUM and ΔPMB. We have angles ∠B=35°,∠U=62°,∠P=21°. The angles are ∠1=56° and ∠2=62°.
Given that,
In picture there is a triangle with the intersection line in between the triangles.
Triangle PUB is divided into 2 triangles that is ΔPUM and ΔPMB.
We have angles
∠B=35°,∠U=62°,∠P=21°
We have to find the angle of angle 1 and 2.
We know,
In triangle sum of the 3 angles is 180°.
Now, we take ΔPMB
We find the other angle of M.
21°+35°+M=180°
M=180°-21°-35°
M=180°-56°
M=124°
So, now we can find the angle 1.
the straight line has a angles of 180°.
124°+∠1=180°
∠1=180°-124°
∠1=56°
Now, we find angle 2.
Take ΔPUM
62°+∠1+∠2=180°
62°+56°+∠2=180°
∠2=180°-62°-56°
∠2=180°-118°
∠2=62°
Therefore, the angles are ∠1=56° and ∠2=62°.
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Since 2 is further left on a number line than 5, 2 < 5. Let’s consider the opposites of these numbers.
Identify the opposite of 2 on the number line.
Identify the opposite of 5 on the number line.
Using your results, which statement is true?
Since –2 is further
.
Write a two column proof for this:
Using angle addition postulate when ∠1 ≅ ∠4 it is proved that ∠2 ≅ ∠3.
As given in the question,
Given: ∠1 ≅ ∠4. Prove ∠2 ≅ ∠3.
(Using angle addition postulate)
Statements Reasons
1. ∠1 ≅ ∠4 Given
2. ∠1 = 180 - ∠2 Being supplementary angles (angle addition postulate)
3. ∠4 = 180 - ∠3 Being supplementary angles (angle addition postulate)
4. 180 - ∠2 = 180 - ∠3 Substituting Statements 2 & 3 into Statement 1.
5. ∠2 = ∠3 Simplifying Statement 4 algebraically.
In statement 4, the constants 180 cancel out from either of left hand side (LHS) and right hand side (RHS). Thus the equation gets simplified to Statement 5. It is worthwhile to mention that Supplementary angles or linear pair always sum up to 180° in measure. Additionally linear pair form a straight line together.
Therefore, using angle addition postulate when ∠1 ≅ ∠4 it is proved that ∠2 ≅ ∠3.
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I need help on Question 3. Ignore the other ones please. Thank you so much!! 15 points if you get it right!
The value of x and y for given equation are (2,15) and (12,24).
Using hit and trial method, we can calculate that the values of given equation are (2,15) and (12,24)
What is hit and trial method?
The hit and trial approach is used to balance chemical equations by selecting the least whole number coefficient. tally the instances of each ingredient on either side of a reaction. The element with the lowest frequency of recurrence is considered to be balanced.
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List all the factors of 12.
Answer: The factors of 12 are 1, 2, 3, 4, 6, and 12
Hope this helps!
Answer:
The factors of 12 are 1, 2, 3, 4, 6 and 12.
the formula t=((sqrt(h))/(4)) represents the time t in seconds that is takes an object to fall from a height of h feet , if a rock falls from 125 feet , estimate how long it will take the rock to hit the ground , estimate the square root to the nearest integer .
The time taken by the rock to hit the ground is 3 seconds.
It is given in the question that:-
[tex]t=\frac{\sqrt{h} }{4}[/tex]
Where,
t represents the time (in seconds) taken by the object to reach the ground, and
h represents the height from which the object is falling
We have to find the time taken by a rock to hit the ground after falling from a height of 125 feet.
Using the formula given in the question, we can write,
[tex]t=\frac{\sqrt{125} }{4}=\frac{5\sqrt{5} }{4}[/tex]
We know that,
[tex]\sqrt{5}[/tex] ≈ 2.23
Hence, we can write,
t ≈ (5*2.23)/4 ≈ 2.7875 ≈ 3 seconds (estimated to nearest integer)
Hence, it takes around 3 seconds for the rock to hit the ground after falling from a height of 125 feet.
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Find the measures of two supplementary angles if the difference between the
measures of the two angles is 35
Answer:
107.5 and 72.5
Step-by-step explanation:
Which of the following is an equivalent expression of 18x2 +14x + 7?
7(18x2 + 14x)
14x + 18x2 + 7
32x3 + 7
18x2(14x + 7)
An expression which is equivalent to the given expression 18x² +14x + 7 is given by 14x + 18x² + 7.
As given in the question,
Given expression is :
18x² +14x + 7
Simplify all the optional expression to check which one is equivalent to given expression:
a. 7(18x² + 14x)
= 126x² + 98x
Not equivalent.
b. 14x + 18x²+ 7
Rearrange it
18x²+14x + 7 .
Equivalent.
c. 32x³ + 7
Degree is 3.
Not equivalent.
d. 18x²(14x + 7)
= 252x³ +126x²
Not equivalent.
Therefore, an equivalent expression of 18x²+14x + 7 is 14x + 18x²+ 7.
The complete question is:
Which of the following is an equivalent expression of 18x²+14x + 7?
7(18x² + 14x)
14x + 18x²+ 7
32x³ + 7
18x²(14x + 7)
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Help pls!! Will give brainlyist
Answer: The correct answer is B.
Step-by-step explanation:
To evaluate this expression you must divide x-1 though the expression or factor out the upper half of the equation and cancel out what is necessary.
The division method: attached below :)
the scale of a map is 1:10000000. what is the real distance between two cities if the distance between them is 1.7dm
Answer:
See below:
Explanation:
1.7 dm = .17 m assuming dm is decimeter
.17m * 10^7 scale = 1.7 x 10^6 m = 1.7 x 10^3 km = 1700 km
suppose that the weight, x, in pounds, of a 40-year-old man is a normal random variable with mean 147 and standard deviation 16. calculate p(120≤x≤153). round your answer to four decimal places.
0.6004 is standard deviation of equation .
Why is there a standard deviation?
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.An individual collection of data is compared to the average of several other sets of data using the standard deviation. You can compute two different forms of standard deviation: When data are gathered from every person in a population or collection, it is the population standard deviation.=0.6004$P(120≤X≤153)=0.6004
The mean is μ=147, and the standard deviation is σ=16.
0.6462−0.0458=0.6004.
Thus, P(120≤X≤153)=0.6004.
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Write and solve an equation to solve the problem.
Lisa is 4 centimeters taller than her friend lan. lan is 8 centimeters taller than Jim. Every month, their heights increase by 2 centimeters. In 4 months, the sum of lan's and Jim's heights will be 170 centimeters more than Lisa's height. How tall is lan now? Let h be lan's height today in centimeters.
(h+8)( )+8=( )+8+170
Ian is ___ centimeters tall now.
Ian is 144 centimeters tall now by solving the equation.
What is an equation?A mathematical statement called an equation includes the sign "equal to" between two expressions with equal values.
Let Lisa, Ian, and Jim's real heights are L, I, and J, respectively.
Lisa's friend Ian is 4 centimeters taller than her, therefore L=4+I
In the sentence "Ian is 8 cm taller than Jim.": I=8+J,
Hence, J=I-8
Thus, Lisa, Ian, and Jim are 4+I, I, and I-8 correspondingly in height.
Since their heights increase by 2 cm every 4 months, this results in an 8-centimeter height increase.
Thus, after four months, Lisa, Ian, and Jim reach the following heights:
4+I+I+8, I+8, and I-8+8 that equal to I+12, I+8, and I respectively
"The total of Ian's and Jim's heights will be 140 centimeters more than Lisa's height in four months" means:
(I + 8) + I = 140 + (I + 12)
⇒2I + 8 = 152+I
⇒I = 144
⇒I=152-8
=144
Therefore, Ian is 144 centimeters tall now.
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Math
Language arts
Geometry B.10 Midpoint formula: find the midpoint 2YG
Submit
Recommendations
Skill p
B(-2, -13) and C(-3, 6) are the endpoints of a line segment. What is the midpoint M of that
line segment?
Write the coordinates as decimals or integers.
M =
Please help
m=x1+x2/2 or m=y1+y2/2
hope you understand
8 + 3x = 1 + 7.9x can someone help me out?
GROUP LIKE TERMS TOGETHER.
[tex]3x - 1.79x = 1 - 8 \\ 1.21x = - 7 \\ \frac{1.21x}{1.21} = \frac{ - 7}{1.21 \\ } \\ x = 5.7851239669[/tex]
Answer:
x=[tex]\frac{10}{7}[/tex]
Step-by-step explanation:
8 + 3x = 1 + 7.9x
1. multiply everything by 10 so there is no longer a decimal in the equation
80+30x=10+79x
2. get the x on one side so we -10 and 30x from both side
70=49x
3. divide by 49 on each side as we want to find the value of x
[tex]\frac{70}{49}[/tex]=x
4. the fraction can be simplified to
[tex]\frac{10}{7}[/tex]=x
4. the final answer is
[tex]\frac{10}{7}[/tex]=x
what is 369 962 to the nearest 100
Answer:
370000
Step-by-step explanation:
So it would go from 962-1000. So 370000
given the expression 3x^4 - 5x + 2 state what each of the following represents
-5
2
3x^4
4
Given the algebraic expression 3x⁴ - 5x + 2, each of following represents:
-5 = coefficient.2 = constant3x⁴ = monomial4 = exponent.What is an algebraic expression?An algebraic expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables, numerical quantities (constants), accompanied with the use of different mathematical operations.
What is a coefficient?In Mathematics, a coefficient simply refers to a constant quantity or numerical value (number or numeral) that is typically placed before the variable in an algebraic expression.
In conclusion, an exponent is an operation that raises a numerical value or quantity to the power of another and it is generally written as bⁿ.
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Help please it's true or false
Answer:true
Step-by-step explanation:
because the first one
need help with this, thanks
The error is that vertical angles are congruent, and don't necessarily add to 180°. Vertical angles only add to 180° if they are right angles.
[tex]13x+45+19x+3=180 \\ \\ 32x+48=180 \\ \\ 32x=132 \\ \\ x=33/8[/tex]
Answer:
x = 7
Step-by-step explanation:
Vertical Angle Theorem
When two straight lines intersect, they form two pairs of angles. The vertically opposite (non-adjacent) angles are congruent.
Angles on a Straight Line Theorem
The sum of angles formed on a straight line is equal to 180°.
The error made is confusing the Vertical Angle Theorem with the Angles on a Straight Line Theorem. To find x, we should either:
Equal a pair of vertical angles and solve for x, orEqual the sum a pair of angles that form a straight line to 180° and solve for x.Applying the Vertical Angle Theorem:
[tex]\boxed{\begin{aligned} (13x+45)^{\circ} &=(19x+3)^{\circ} \\13x+45&=19x+3\\13x+42&=19x\\42&=6x\\x&=7\end{aligned}}[/tex]
Applying the Angles on a Straight Line Theorem:
[tex]\boxed{\begin{aligned}(6x+2)^{\circ}+(19x+3)^{\circ}&=180^{\circ}\\6x+2+19x+3&=180\\25x+5&=180\\25x&=175\\x&=7\end{aligned}}[/tex]
Therefore, the value of x is [tex]\boxed{x=7}[/tex] .