Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{294}}}}}[/tex]
Step-by-step explanation:
PEMDAS is a acronym which helps you to remember the order of operations.
PEMDAS stands for :
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Let's solve
[tex] \sf{15 \times 18 + 12 + 3 + 9}[/tex]
Multiply the numbers : 15 × 18 = 270
⇒[tex] \sf{270 + 12 + 3 + 9}[/tex]
Add the numbers : 270 + 12 + 3 + 9
⇒[tex] \sf{294}[/tex]
Hope I helped!
Best regards!!
Answer:
This would equal 294
Step-by-step explanation:
i added them up
Please Answer Both Questions
Answer:
c. 48 packages
d. Possibilities:
1 x 28 = 28
2 x 14 = 28
4 x 7 = 28
7 x 4 = 28
14 x 2 = 28
28 x 1 = 28
Possible combinations:
17, 1, 28
17, 2, 14
17, 4, 7
17, 7, 4
17, 14, 2
17, 28, 1
Step-by-step explanation:
c. 127 employees get 3 uniforms each, meaning a total of 127 * 3 = 381 uniforms
The uniforms come in packs of 8, so dividing 381 by 8, we get:
381/8 = 47.625
However, you probably can't order a portion of a package, so you must round up to 48 packages. There will be 3 uniforms left over.
d. The divisors of 28 are 1, 2, 4, 7, 14, and 28. All I did was enumerate the six possibilities.
If g(x)=a x f(x+b) how is f(x) transformed to get g(x)
Answer:
a: -2f(x+4)
Step-by-step explanation:
Took the quiz, got 100%.
The function f(x) = ∛x is transformed to obtain g(x) = -2f(x + 4). Option A is correct.
The function f(x) = ∛x is shifted horizontally to the left by 4 units.
This means that every point on the graph of f(x) is moved 4 units to the left.
After the horizontal shift, the function is reflected vertically and stretched vertically by a factor of 2.
The reflection indicates that the graph is flipped upside down, and the stretching means that the graph is elongated vertically by a factor of 2.
By applying these transformations to the function f(x) = ∛x, we obtain the function g(x) = -2f(x + 4).
The negative sign indicates the vertical reflection, and the factor of 2 represents the vertical stretching.
The horizontal shift of 4 units is applied to the argument of the function, which is (x + 4)
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Suppose "35" cars start at a car race. In how many ways can the top 3 cars finish the race?
The number of different top three finishes possible for this race of 35 cars is 39,270. (Use integers for any number in the expression.)
Answer:
The value is [tex]\left 35 } \atop }} \right. P_3 = 39270[/tex]
Step-by-step explanation:
From the question we are told that
The total number of cars is [tex]n = 35[/tex]
The number cars considered is [tex]r = 3[/tex]
Generally the number of different top three finishes possible for this race of 35 cars is mathematically represented as
[tex]\left n } \atop }} \right. P_r = \frac{n!}{(n - r) !}[/tex]
[tex]\left 35 } \atop }} \right. P_3 = \frac{35! }{(35 - 3) !}[/tex]
[tex]\left 35 } \atop }} \right. P_3 = \frac{35 * 34 * 33 * 32! }{32 !}[/tex]
[tex]\left 35 } \atop }} \right. P_3 = 39270[/tex]
A linear trend equation is used to represent time series values when the data are changing by equal what? a. proportions b. amounts c. percentsd. percents and proportions
Answer: Amounts
Step-by-step explanation:
Time series analysis are the method which are used by researchers to analyze the time series data so as to get the features of the data and to also derive meaningful statistics.
A linear trend equation is used to represent time series values when the data are changing by equal amounts.
A ladder 10 m long,leans against a vertical wall at an angle of 70° to the ground.if the ladder slips down the wall 4m,find,correct to 2 significant figure
(a) the new angle which the ladder makes with the ground
(b) the distance the ladder slipped back on the ground from it's original position
Answer to part (a) is: 33 degrees
Answer to part (b) is: 5 meters
=============================================
Explanation:
Check out the diagram below.
For now, focus only on triangle ABC. The ladder is segment AC = 10. We first need to find the length of [tex]AB = h_1[/tex] which is the initial height of the ladder.
sin(angle) = opposite/hypotenuse
sin(70) = h/10
h = 10*sin(70)
h = 9.396926 approximately
Subtract off 4 since the ladder slips 4 meters down the wall
h-4 = 9.396926-4
h-4 = 5.396926
which is the new height the ladder reaches. The hypotenuse stays the same
sin(angle) = opposite/hypotenuse
sin(theta) = 5.396926/10
theta = arcsin(5.396926/10)
theta = 32.662715
theta = 33 degrees when rounding to 2 significant figures
This is the value of [tex]\theta_2[/tex] in the diagram below.
---------------------------------
We'll use the cosine rule with the old theta value [tex]\theta_1[/tex]
cos(angle) = adjacent/hypotenuse
cos(70) = x/10
x = 10*cos(70)
x = 3.420201 is the approximate distance the foot of the ladder is from the wall. This is before the ladder slips.
After the ladder slips, we use the new angle value [tex]\theta_2[/tex]
cos(angle) = adjacent/hypotenuse
cos(32.662715) = x/10
x = 10*cos(32.662715)
x = 8.418622
Subtract the two x values
8.418622-3.420201 = 4.998421
which gives the approximate distance the foot of the ladder moved (the distance from point C to point E in the diagram)
This rounds to 5.0 or simply 5 when rounding to 2 significant figures.
Which symbol is needed between -2? |-3| to make a true statement? PLS HELP
60 points!!!!!!!!!!!!!!!
A. <
B. >
C. =
Answer:
[tex]\Huge \boxed{<}[/tex]
Step-by-step explanation:
-2 ? |-3|
Solve for absolute value.
Apply rule : |-a| = a
|-3| = 3
-2 ? 3
-2 is less than 3.
The less than symbol is “<”.
-2 < 3
Please help Simplify (3^6)^18
Answer:
when we put an exponent on a number which already has an exponent, the exponents are multiplied
we have: [tex]3^{6^{18} }[/tex]
= [tex]3^{108}[/tex]
(3)^6×18
(3)^108
now if you want to further simplify it then just simply calculate 3^108 on the calculator
to make it clear (3^6)^18 and 3^6^8 are two different situations
in the first one the power will be multiplied by the second power
and in the second one 6 will be multiplied by itself 8 times
Which of the following circumstances would likely make factoring the best method for solving a quadratic equation?
Question 3 options:
A quadratic that is prime
The leading coefficient is zero
The leading coefficient is not 1 and the constant is a large number
The difference of 2 perfect squares
Answer:
Option D.
Step-by-step explanation:
We need to find the circumstances that would likely make factoring the best method for solving a quadratic equation.
A quadratic equation is prime if its factors can not possible. So, option A is incorrect.
In a quadratic equation leading coefficient can not be zero. So, option B is incorrect.
For large numbers (coefficient or constant), quadratic formula is best method. So, option C is incorrect.
The difference of 2 perfect squares is:
[tex]x^2-a^2=(x-a)(x+a)[/tex]
In this case factoring is the best method.
Therefore, the correct option is D.
Making a certain shade of paint requires mixing 3 parts silver with 4 parts green. Meg uses this data to start this table of equivalent ratios.
Answer:
6:8 and 9:12
Step-by-step explanation:
The equivalent ratios of the given quantity of silver parts of paint to green which is 3:4 are: 6:8 and 9:12.
What are Equivalent Ratios?When compared to one another, equivalent ratios are defined as having the same values.
For example, 8/16, 4/8 and 1/2 re equivalent ratios because:
Given:
The table that shows the ratio of the number of parts silver to number of parts green as 3 parts silver to 4 parts green, then
ratio = 3:4.
This means that for 3 parts of silver paint, we would require 4 parts of green paint to give the shade of paint that is needed.
so,
6/8 = 3/4
9/12 = 3/4
Thus, 6/8 = 9/12 = 3/4, which is equivalent.
Hence, the ratios that are equivalent to 3 parts silver paint to 4 parts green paint are: 6:8 and 9:12.
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Find the value of x. A. 5√2/2 B. 5 C. 10 D. 10√2
Answer:
C
Step-by-step explanation:
Note that the right triangle has two tick marks.
This means that the sides are equivalent.
Therefore, this is a 45-45-90 triangle.
In a 45-45-90 triangle, the side lengths are n, and the hypotenuse is n√2
Since n is 5√2, then the hypotenuse x is n√2. Thus:
[tex]x=n\sqrt2\\x=(5\sqrt2)\sqrt2[/tex]
Simplify:
[tex]x=5(2)=10[/tex]
The answer is C :)
A........ divides a two - dimensional shape into two congruent shapes
Answer:
A diagonal. (A rectangle is divided into two triangles by a diagonal, for example.)
The diagonal of a triangle divides a two dimentional shape into two congruent shapes.
The congruent shapes are equally the same
Based on the similar triangles shown below, Theodore claims that ∆TUV is transformed to ∆WXY with a scale factor of 32. Is Theodore correct? A Yes, the triangles are similar with a scale factor of 32. B No, the triangles are similar with a scale factor of 21. C No, the triangles are similar with a scale factor of 23. D No, the triangles are similar with a scale factor of 43.
*Correct Question:
Based on the similar triangles shown below, Theodore claims that ∆TUV is transformed to ∆WXY with a scale factor of 3/2. Is Theodore correct?
A. Yes, the triangles are similar with a scale factor of 3/2.
B. No, the triangles are similar with a scale factor of 2/1.
C. No, the triangles are similar with a scale factor of 2/3.
D. No, the triangles are similar with a scale factor of 4/3.
Answer:
C. No, the triangles are similar with a scale factor of 2/3.
Step-by-step explanation:
∆TUV is the original triangle. After transformation, the size reduced to give us ∆WXY. This means ∆TUV was reduced by a scale factor to give ∆WXY. The scale factor should be a fraction, suggesting, the original size of the ∆ was reduced upon transformation.
Thus, the ratio of their corresponding sides = the scale factor.
This is: [tex] \frac{8}{12} = \frac{16}{24} = \frac{12}{18} = \frac{2}{3} [/tex]
If you multiply the side length of ∆TUV by ⅔, you'd get side length of ∆WXY.
So, Theodore is wrong.
Verify that the vector X is a solution of the given homogeneous system. X' = −1 1 25 1 −1 X; X = −1 5 e−6t/5 For X = −1 5 e−6t/5, one has
Answer: Find answer in the attached file
Evaluate R C F · dr, where F(x, y, z) = 5xi − 5yj − 3zk and C is given by the vector function r(t) = hsin t, cost, ti, where 0 ≤ t ≤ π.
Answer:
[tex]\mathbf{ - \dfrac{3 \pi^2}{2}}[/tex]
Step-by-step explanation:
Given that:
F(x, y, z) = 5xi - 5yj - 3zk
The objective is to evaluate the [tex]\int _c F \ dr .C[/tex]
and C is given by the vector function r(t) = (sin t, cost, t) where 0 ≤ t ≤ π
[tex]F(r(t)) = 5 \ sint \ i - 5 \ cost \ j - 3t \ k[/tex]
∴
[tex]\int_c F . \ dr = \int ^{\pi}_{0} ( 5 \ sint \ i - 5 cos t \ j - 3 t \ k ) ( cos \ t , - sin \ t , 1 ) \ dt[/tex]
[tex]=\int ^{\pi}_{0} ( 5 \ sint \ cost+ 5 cos t \ sin t - 3 t) dt[/tex]
[tex]=\int ^{\pi}_{0} ( 10 \ sint \ cost) \ dt -3 \int ^{\pi}_{0} \ dt[/tex]
[tex]= \int ^{\pi}_{0} ( 10 \ sint \ cost) \ dt - 3 [\dfrac {t^2}{2}]^{\pi}_{0} \ \ dt[/tex]
[tex]= 10 [\dfrac{sin^2 \ t}{2}]^{\pi}_{0} - \dfrac{3}{2}(\pi)^2[/tex]
By dividing 2 with 10 and integrating [tex]= 10 [\dfrac{sin^2 \ t}{2}]^{\pi}_{0}[/tex]; we have:
[tex]=5(sin^2t -sin^2 0) -\dfrac{3 \pi^2}{2}[/tex]
[tex]=5(0) -\dfrac{3 \pi^2}{2}[/tex]
[tex]= 0 - \dfrac{3 \pi^2}{2}[/tex]
[tex]\mathbf{= - \dfrac{3 \pi^2}{2}}[/tex]
Suppose a prediction equation was built on training data yielding:
y_hat = 145.5 -5.5*x
Given this small set of test data, calculate the RMSE.
x у
1 10.36 87.87
2 9.96 89.83
3 12.50 71.61
a. 1.98.
b. 3.04.
c. 9.21.
d. 5.37.
Answer:
3.04
Step-by-step explanation:
Given the prediction equation:
y_hat = 145.5 -5.5*x
- - - - x - - - - - - - - - у
1 - - 10.36 - - - - 87.87
2 - - 9.96 - - - - 89.83
3 - - 12.50 - - - - 71.61
1) y_hat = 145.5 -5.5*(10.36)
y_hat = 145.5 - 56.98 = 88.58
2) y_hat = 145.5 -5.5*(9.96)
y_hat = 145.5 - 54.78 = 90.72
3) y_hat = 145.5 -5.5*(12.50)
y_hat = 145.5 - 68.75 = 76.75
Root mean squared error (RMSE) :
Number of observations (n) = 3
√(Σ(y_hat - y)^2) / n
y_hat = predicted value
y = actual value
Σ[(88.58-87.87)^2+(90.72-89.83)^2+(76.75-71.61)]
Σ(0.71^2) + (0.89^2) + (5.14^2)
27.7158 / 3 = 9.2386
√9.2386
= 3.0395065
= 3.04
which statement is true about the value of |-5|
WILL GIVE BRAINLIEIST!!
The efficiency of a motor can be measured by the percent of input power that the motor uses. E(c) models the efficiency (in percentage points) of a certain motor as a function of the power inputs current c (in amperes). Match each statement with the feature of the graph that most closely corresponds to it.
Answer:
The matches are:
Feature: Increasing or decreasing interval (specifically, a decreasing interval)
Statement: As the input power's current grows beyond 1 ampere...
Feature: Relative minimum or maximum (specifically, relative maximum)
Statement: At its most efficient, the motor uses...
Feature: x-intercept
Statement: The motor loses all efficiency when the current...
Step-by-step explanation:
The first statement describes a decreasing interval, specifically the decreasing efficiency beyond 1 ampere of input current
The second statement describes a relative maximum, specifically the maximum efficiency at an input current of 1 ampere
The third statement describes an x-intercept, specifically the efficiency hitting 0% when the input current is ≥ 3 amperes
Answer:
(a) x -intercept with the last statement (the one at the bottom)
(b) Relative maximum with the second (middle) statement.
(c) Increasing or decreasing with the first (top) statement.
See details below:
Step-by-step explanation:
(a) The x-intercept goes with the info on what happens when the graph crosses the horizontal axis, so it goes with the third statement given:
The motor loses all efficiency when the current hits 3 amps.
(b) Relative max: agrees with what happens at the maximum the curve shows reaching approximately 50% value in the vertical scale:
At its most efficiency the motor uses about 50% of the input power
(c) Increasing or decreasing interval: The function clearly increases from values of the horizontal variable starting at around 0.4, up to a value of 1, and from then onwards it decreases. So it agrees with:
As the input grows more than 1 ampere, the motor becomes less efficient.
please help me with this question
Answer:
[tex] {\sqrt[ 3 ]{x^{2} } }•{ \sqrt[4] {{y}^{3}} }[/tex]
Explanation-
As,
[tex]a^{\frac{1}{n} } = \sqrt[n]{a} [/tex]
and
[tex]a^{-n}=1/a^n[/tex]
is 289 a prime number
Answer:
No
Step-by-step explanation:
Factors of 289 are = 1, 7, 289
answer
no
explanation
the factor of 289= 1 , 17
Wich expression is equivalent to h+0.48h+0.58?
A.0.06h
B.0.58 + 1.48h
C.h + 1.06
D.2.06h
Answer:
B. 0.58 + 1.48h
Step-by-step explanation:
h+0.48h+0.58
=(1h+0.48h)+0.58
=1.48h +0.58
What is a key distinction between parametric tests and nonparametric tests in terms of scales of measurement
Answer:
Parametric tests are used for interval and ratio data and Non parametric tests are used for ordinal and nominal data.
Step-by-step explanation:
Parametric tests are used for interval and ratio data and Non parametric tests are used for ordinal and nominal data.
The interval data shows data with differences or intervals.
The ratio data is the one in which statistical inferences is used and can be added ,subtracted , multiplied, or divided.
Ordinal data is one in which we measure quantitative data such as height , weight but is in order.
Nominal data is one in which we measure quantitative data such as hair color eye color without order or which does not require order or sequence.
A standard number cube is rolled. Calculate: P(rolling a 5)
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
Total no. of outcomes = 1,2,3,4,5,6
No. of times 5 is on the cube =1
Therefore, probability of getting a 5 = [tex]\frac{1}{6}[/tex]
Starbucks repurchased over $7,208.7 million of its common stock in 2018. Did this repurchase increase or decrease Starbucks’ ROE?
Write the sentence as an equation.
61 is equal to 268 added to y
Type a slash ( 7 ) if you want to use a division sign
Answer:
y= -207
Step-by-step explanation:
61 = 268 + y
Collect like terms
y= 61 - 268
Simplify
= -207
y= -207
Alternatively,
61 = 268 + y
Subtract 268 from both sides
61 - 268 = 268 + y - 268
-207 = y
Therefore,
y= -207
A fisherman leaves his home port and heads in the direction N 70 ° W. He travels d1 = 40 mi and reaches Egg Island. The next day he sails N 10 ° E for d2 = 65 mi, reaching Forrest Island.
(a) Find the distance between the fisherman's home port and Forrest Island. (Round your answer to two decimal places.)
(b) Find the bearing from Forrest Island back to his home port. (Round your answer to one decimal place.)
S ° E
Answer:
A)82.02 mi
B) 18.7° SE
Step-by-step explanation:
From the image attached, we can see the angles and distance depicted as given in the question. Using parallel angles, we have been able to establish that the internal angle at egg island is 100°.
A) Thus, we can find the distance between the home port and forrest island using law of cosines which is that;
a² = b² + c² - 2bc Cos A
Thus, let the distance between the home port and forrest island be x.
So,
x² = 40² + 65² - 2(40 × 65)cos 100
x² = 1600 + 4225 - (2 × 2600 × -0.1736)
x² = 6727.72
x = √6727.72
x = 82.02 mi
B) To find the bearing from Forrest Island back to his home port, we will make use of law of sines which is that;
A/sinA = b/sinB = c/sinC
82.02/sin 100 = 40/sinθ
Cross multiply to get;
sinθ = (40 × sin 100)/82.02
sin θ = 0.4803
θ = sin^(-1) 0.4803
θ = 28.7°
From the diagram we can see that from parallel angles, 10° is part of the total angle θ.
Thus, the bearing from Forrest Island back to his home port is;
28.7 - 10 = 18.7° SE
What value(s) of x will make each equation below true?
2x – 6 = 3x +1-x-7
The answer is any value that you put in for x would make the equation true. When you simplify the whole equation it looks like this: 2x - 6 = 2x - 6, therefor you could replace x with any value.
Two integers are relatively _________ if and only if their only common positive integer factor is 1.
Answer:
Two integers are relatively primes if and only if their only common positive integer factor is 1.
Step-by-step explanation:
The prime number is one whose only divisor is 1 and itself.
The prime factors of a whole number are the exact prime divisors of that whole number. In other words, every composite number can be written as a multiplication of two or more prime factors.
So, two integers are relative primes if they have no prime factor in common, or, put another way, if they have no common divisor other than 1.
So, two integers are relatively primes if and only if their only common positive integer factor is 1.
A 35 foot tree casts a 13 foot shadow. What is the degree of elevation for the sun?
Answer:
tan (thita) = 35/13
Step-by-step explanation:
Tan( angle) = opposite/ adjacent
Tan( angle) = 35/13
Angle = arc tan 35/13
Angle = 69.624 degrees
Round the answer as needed.
Choose the best definition for the following term: variable
Step-by-step explanation:
a variable is a quantity that may change within the context of a mathematical problem or experiment
I hope this was helpful
LSAT test scores are normally distributed with a mean of 152 and a standard deviation of 10. Find the probability that a randomly chosen test-taker will score 142 or lower. (Round your answer to four decimal places.)
Answer:
the probability that a randomly chosen test-taker will score 142 or lower = 0.8643
Step-by-step explanation:
We are given;
Data point; x = 142
Mean; μ = 153
Standard deviation; σ = 10
So,let's find the z-score using;
z = (x - μ)/σ
z = (142 - 153)/10
z = -1.1
From the z-distribution table attached, the probability is;
P(z < -1.1) = 1 - 0.13567 ≈ 0.8643