In the given triangle, length of AC = 12.3 units
α= 45⁰ and θ = 45⁰
Using Pythagoras theorem,
[tex]AC^{2} = AB^{2} + BC^{2}[/tex]
[tex]AC^{2}[/tex] = 9 + 144
AC = 12.37
Now, to find the angles:
AC is the diagonal.
Then AD=BC and AB=CD
And ∠ABC=∠BCA=∠CDA=∠DAB=90⁰
In ΔABC and ΔADC
∠ABC=∠ADC (Angle of rectangle)
AB=DC (Opposite side of rectangle)
AC=AC (Common side)
∴ΔABC≅ΔADC
∴∠ACD=∠ACB
∵∠ACD+∠ACB=90⁰ ..........[Angle ACB is the angle of rectangle]
∴2∠ACD=90⁰
⇒∠ACD=45⁰
⇒θ = 45⁰
similarly, α = 45⁰
Pythagoras theorem:
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle.
This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation:
[tex]a^{2} + b^{2} = c^{2}[/tex]
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Ryan delivers flowers to two customers. He drives for 12 minutes at an average speed of
40 miles per hour to reach his first customer. He then drives for 15 minutes at an average
speed of 50 miles per hour to reach his second customer. During the 27 minutes of driving
time, how many total miles does Ryan drive?
Answer:20.5 miles
Step-by-step explanation:
the formula for distance, rate (speed), and time is
Distance=rate×time
D=40 (this is the speed he was going for the first customer) × [tex]\frac{12}{60}[/tex] (time)
the time is 12/60 because we the speed was in miles per HOUR and the time was in miles per MINUTE. To convert minutes to hours, we divide by 60.
D=40× [tex]\frac{12}{60}[/tex]
D=48/6
D=8 miles
Second trip:
D= 50×[tex]\frac{15}{60}[/tex]
D=50×[tex]\frac{1}{4}[/tex] (15/60 simplified is 1/4)
D= 12.5 miles
ANSWER: 8 miles + 12.5 miles = 20.5 miles
let z be standard normal random variable. let v be chi-squared random variable with d degrees of freedom. let x and v be independent random variables. show that has student t distribution with $d$ degrees of freedom.
let z be standard normal random variable. let v be chi-squared random variable with d degrees of freedom. let x and v be independent random variables. [tex]$= \frac{1}{\sqrt{2\pi}}\int_{0}^{\in[/tex]
Let [tex]$X$[/tex]and [tex]$V$[/tex] be independent random variables.
[tex]$X \sim N(0,1)$[/tex] , [tex]$V \sim \chi^2(d)$[/tex]
We know that for a standard normal random variable [tex]$X$[/tex] and a [tex]$\chi^2$[/tex] random variable [tex]$V$[/tex] with [tex]$d$[/tex] degrees of freedom, the random variable [tex]$T$[/tex] given by:
[tex]$T = \frac{X}{\sqrt{\frac{V}{d}}}$[/tex]
has a student t-distribution with d degrees of freedom.
This can be seen by the following calculation:
[tex]$f_T(t) = \int_{-\infty}^{\infty} f_X(xt)\frac{1}{\sqrt{2\pi v}}e^{-\frac{v}{2}}\frac{v^{d/2}}{\Gamma(d/2)}\frac{1}{v^{d/2}}e^{-\frac{v}{2d}t^2}dv$[/tex]
[tex]$= \frac{1}{\sqrt{2\pi}}\int_{0}^{\in[/tex]
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The Smiths both work and their total household income is £36,000 per annum.
Their annual bills work out at £16,000 per annum.
What percentage of their annual income goes on bills to 2 decimal places?
%
Answer:
44.44 %
Step-by-step explanation:
16 000 / 36 000 = .4444 = 44.44%
In two common species of flowers, A and B, the proportions of flowers that are blue are papa and pbpb , respectively. Suppose that independent random samples of 50 species-A flowers and 100 species-B flowers are selected. Let pˆap^a be the sample proportion of blue species-A flowers and pˆbp^b be the sample proportion of blue species-B flowers. What is the mean of the sampling distribution of pˆa−pˆbp^a−p^b ?
As per the given distribution, the mean of the sampling distribution is Pa - Pb
The term mean in distribution refers adding all numbers in the data set and then dividing by the number of values in the set.
Here we have given that the proportions of flowers that are blue are papa and pbpb , respectively.
And we need to find the mean of the sampling distribution
While we looking into the given question the mean of a sampling distribution is the population mean from which values are sampled.
Here for a population of mean µ, then the mean of the sampling distribution is μx
=> μα = μ
Here from the given parameters, let us consider that then independent random samples of 50 species-a flowers and 100 species-b flowers are selected
Then it can be written as Pa refers sample proportion of blue specie - a and Pb refers sample proportion of blue specie - b
Therefore, the resulting mean is Pa - Pb
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Zaida purchased a used car for $6,500. State tax was 4%, 100 point inspection was $72, $45 for license plate, and $37 for state emissions testing. How much is the total amount paid for the used car plus expenses?
The total amount paid for the used car plus expenses will be $6,914.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Zaida purchased a used car for $6,500.
State tax was 4%, 100 point inspection was $72, $45 for license plate, and $37 for state emissions testing.
Now,
Since, Zaida purchased a used car for $6,500. State tax was 4%, 100 point inspection was $72, $45 for license plate, and $37 for state emissions testing.
Hence, The total amount paid for the used car plus expenses is,
⇒ $6500 + 4% of 6500 + $72 + $45 + $37
⇒ $6500 + $260 + $154
⇒ $6,914
Thus, The total amount paid for the used car plus expenses = $6,914
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The one-to-one function is defined below.
Please help with this answer i’m struggling.
Answer:
<=> (8+9y)x=-y+9
<=> 8x+9yx+y=9
<=> y(9x+1)=9-8x
<=> y=(9-8x)/(9x+1)
domain: 9x+1 [tex]\geq[/tex] 0 <=> x [tex]\geq[/tex] -1/9 => R / {-1/9}
range: R/{-8/9} (horizontal asymptot)
solve the following trigonomic equation for 0 < theta < 2pi
cos(theta) * csc(theta) - 2cos(theta) = 0
pls help
Answer:
To solve the given trigonometric equation, we can start by isolating the cos(theta) term on one side of the equation. We can do this by dividing both sides of the equation by csc(theta):cos(theta) * csc(theta) - 2cos(theta) = 0
cos(theta) * csc(theta) / csc(theta) - 2cos(theta) / csc(theta) = 0 / csc(theta)
cos(theta) - 2cos(theta) / csc(theta) = 0Next, we can combine like terms on the left side of the equation:cos(theta) - 2cos(theta) / csc(theta) = 0
-2cos(theta) / csc(theta) + cos(theta) = 0
(1 - 2 / csc(theta)) cos(theta) = 0Since cos(theta) cannot be equal to 0 (because the angle theta is between 0 and 2pi), the only solution to this equation is:1 - 2 / csc(theta) = 0
1 = 2 / csc(theta)
csc(theta) = 2This means that the value of csc(theta) is equal to 2. To find the value of theta, we can use the inverse cosecant function (arcsec) to solve for theta:theta = arcsec(2)The value of arcsec(2) is approximately 1.047198, which is the solution to the given equation for theta.Note that this is just one solution to the equation, as there may be other solutions for theta depending on the values of the trigonometric functions. It is important to check that the solution falls within the given range of 0 < theta < 2pi.
Tell me which equation is false based on the solution set
Answer: -26=2(3p-5) is false
Step-by-step explanation:
The solution is 4
Substitute in 4 in place of the variables to prove whether its false or true
1/4(4)+17=18
18=18 true
5=4(4)-11
5=16-11
5=5 true
-26=2(3(4)-5)
-26=2(7)
-26[tex]\neq[/tex]14
3(4+4)=24
3(8)=24
24=24 true
-26=2(3p-5) is false
Answer:
The third option is false, because when you plug in 4 for p, you get 14, and 14 is not equal to -26.
Hope this helps! :D
Step-by-step explanation:
Select Strong association, Weak association, or Moderate association to correctly classify each correlation coefficient. Correlationcoefficient Strongassociation Weakassociation Moderate association 0.45 0.95 -0.8 0.10
The correlation coefficient is,
0.45 is a moderate association0.95 and -0.8 are both the strong association0.10 is weak associationThis is the interpretation of the correlation coefficient,
A scatter plot's correlation coefficient evaluates the association between two variables.If the correlation coefficient's sign is positive, the two variables tend to increase or decrease in the same direction. If variable X increases, variable Y increases; conversely, if variable X reduces, variable Y increases. If the correlation coefficient's sign is negative, the two variables have an inverse relationship. This curve or line slopes downward. A correlation coefficient of +1 or -1 is a perfect association. The two variables are totally associated.A strong relationship is defined as a correlation coefficient that is less than +1 but more than 0.7. A coefficient between -0.7 and -1 would be the same.A moderate link is indicated by a correlation coefficient of +0.5 or -0.5. There is no correlation when the correlation coefficient is zero. A correlation coefficient of 0 is a null association.A weak relationship is 3;. similar when the correlation coefficient ranges from -3 to 0.To read more about Correlation coefficient
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Question 5 of 50
If 15% of college students own a television, and 10% of college students own a stereo, and 2% of college students own both a television and a stereo, then the percent of college students that own either a television or stereo is 23%.
True
False
The percentage of students who owns either a television or stereo is given by the set formula P ( A ∪ B ) = 23 %
What is Set Theory Formula?
The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets
The intersection of two sets is a new set that contains all of the elements that are in both sets
The equation is n(A∪B) = n(A) + n(B) - n(A⋂B)
Given data ,
Percentage of college students who owns a television or stereo be represented as = P ( A ∪ B )
Percentage of college students who owns a television is P ( A ) = 15 %
Percentage of college students who owns a stereo is P ( B ) = 10 %
Let the percentage of college students who owns a television and stereo is P ( A ∩ B ) = 2 %
So , the value of P ( A ∪ B ) is calculated as
P (A∪B) = P ( A ) + P ( B ) - P ( A ⋂ B )
Substituting the values in the equation , we get
P (A∪B) = 15 + 10 - 2
On simplifying the equation , we get
P (A∪B) = 25 - 2
P (A∪B) = 23 %
Therefore , the value of P (A∪B) is 23 %
Hence , the percentage of students is 23 %
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Myesha and her children went into a bakery that sells cupcakes for $4.25 each and cookies for $0.75 each. Myesha has $30 to spend and must buy at least 16 cupcakes and cookies altogether. If xx represents the number of cupcakes purchased and yy represents the number of cookies purchased, write and solve a system of inequalities graphically and determine one possible solution.
The system of the equation is written as
xx + yy ≥ 16
$4.25xx + $0.75yy ≤ $30
the graph is attached and the solution from the graph is (5.1, 10.9)
How to write the required equationThe problem is a simultaneous equation of two unknowns with two equations.
The equations are formed as follows
If xx represents the number of cupcakes purchased
yy represents the number of cookies purchased
cupcakes for $4.25 each and cookies for $0.75 each. Myesha has $30
$4.25xx + $0.75yy = $30
buy at least ( ≥ ) 16 cupcakes and cookies altogether
xx + yy ≥ 16
The simultaneous equation
xx + yy ≥ 16
$4.25xx + $0.75yy = $30
One solution from the graph is (5, 11)
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A container that weighs 23 2/5pounds
holds sports equipment. Of the
equipment in the container, of the
1
3
weight is baseball equipment. What is the
weight of the baseball equipment?
The weight of the baseball equipment in the container is 7(4/5) pounds.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Container weight = 23(2/5) pounds
Baseball equipment.
= 1/3 of 23(2/5) pounds
= 1/3 x 117/5
= 39/5
= 7(4/5) pounds
= 7.8 pounds
Thus,
The weight of the baseball is 7.8 pounds.
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Anne Marie will cut a piece of wood that is 2 ½ feet long into ¼ -foot sections. How many sections will result?
Answer:
10
Step-by-step explanation:
2 1/2 divided by 1/4
1. Make improper
5/2 divided by 1/4
2. Keep Change Flip (Multiply by reciprocals)
5/2x4/1
3. Solve!
20/2
4. Simplify
10/1=10
3x + 2y = 4
-2x + 2y = 24
The answer is (-4,8) I just need someone to solve it please
can someone tell me the steps to solving this and tell me what to write my teacher told me “to show work”
Answer:
55 degrees
Step-by-step explanation:
Sum of ALL three angles of a triangle ALWAYS equal 180
rule is 6x+5 will equal the sum of the 2 known angles because of this
6x+5=3x+x+45
6x+5=4x+45
-4x. -4x
2x+5=45
-5. -5
2x=40
/2. /2
x=20
6(20)+5
120+5
125
180-125
55
hopes this helps please mark brainliest
1. if he flips the bottle ten times, how many do you expect to land right side up? justify by either plugging into the formula or using complete calculator notation. round answer to 4 decimal places.
I expect to land right side up using probability is 2.
What is Probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability.
Probability theory, which is widely employed in disciplines including statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy, has given these ideas an axiomatic mathematical formalization.
I expect to land right side up using probability is 10(0.2)
so that the answer is 2.
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applying the law of cross-cutting relations to the rock pictured above, what is the order (first to last) in which the rock units a-d formed? note that all of the dark-colored rock should be considered part of unit d. group of answer choices a, b, c, d a, c, b, d d, c, b, a d, a, c, b b, c, a, d
unit D must be the youngest rock unit and the order of formation must be A, B, C, D
The Law of Cross Cutting Relations states that any feature (such as a fault or a like) that cuts across a rock unit must be younger than the rock unit.
In the picture, the dark colored rock (unit D) cuts across all of the other rock units (A, B, and C).
Therefore, unit D must be the youngest rock unit and the order of formation must be A, B, C, D.
Therefore, the order of formation is A, B, C, D.
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Let be independent random variables with the common distribution function F and suppose they are independent of a geometric random variable with parameter p. Let M = max(x1,....,xN) (a) Find P{M<} by conditioning on N (b) Find P(M1} (d) Use (b) and (c) to rederive the probability you found in (a).
suppose they are independent of a geometric random variable with parameter p. Let M = max(x1,....,xN) (a) Find P{M<} by conditioning on N is nλe^(-nλx)
Given fx (x) = λe^λx
Fx (x) = 1 – e^-λx x…0
To find distribution of Min (X1,….Xn)
By applying the equation
fx1 (x) = [n! / (n – j)! (j – 1)!][F(x)]^j-1[1-F(x)]^n-j f(x)
For minimum j = 1
[Min (X1,…Xn)] = [n!/(n-1)!0!][F(x)]^0[1-(1-e^-λx)]^n-1λe^-λx
= ne^[(n-1) λx] λe^(λx)
= nλe^(-λx[1+n-1])
= nλe^(-nλx)
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The elephants at the Norfolk Zoo are fed 1/2 of a barrel of corn each day. The buffalo are fed 7/10 as much corn as the elephants. How many barrels of corn are the buffalo fed each day?
Addition
Subtraction
Multiplication
Division
If buffalo are fed 7/10 as much corn as the elephants, then they are fed with 7/20 barrels of corn each day.
How to solve word problems?
Recognize the issue, including all the terminology used to describe it. Recognize what we need to look for, Recognize the issue's context.
Convert the issue into an equation. Give the unknown a variable (or variables) to symbolize, Indicate exactly what the variable stands for.
Put the strategy into action and find a solution.
Given:
Elephants at the Norfolk zoo are fed = 1/2 of the barrel
Buffalo are fed 7/10 as much corn as the elephants = 7/10 * Elephants fed
= 7/10 * 1/2
= 7/20
Therefore, If buffalo are fed 7/10 as much corn as the elephants, then they are fed with 7/20 barrels of corn each day.
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What is the end behavior for the function 7 - 3x5 - 5x³?
O Up and Up
Down and Down
O Up and Down
O Down and Up
What is the difference between the keys on Javanese metallophones and Balinese metallophones?
A. Javanese metallophones have thicker wooden keys than Balinese ones.
B. Balinese metallophones have thicker metal keys than Javanese ones so they produce a brighter sound.
C. Balinese metallophones have thicker wooden keys than Javanese ones.
D. Javanese metallophones have thicker metal keys than Balinese ones so they produce a brighter sound.
Balinese metallophones have thicker metal keys than Javanese ones so they produce a brighter sound. therefore correct answer is B.
A metallophone is any musical instrument in which the sound- producing body is a piece of metal( other than a substance string), conforming of tuned essence bars, tubes, rods, coliseums, or plates. ultimate repeatedly the metal body is struck to produce sound, generally with a mallet, but may likewise be triggered by discordance, keyboard action, or other means.
Metallophones have been used in music in Asia for thousands of spells. There are several different types used in Balinese and Javanese gamelan ensembles, containing the gender, gangsa and saron. These devices have a single row of bars, tuned to the distinctive pelog or slendro scales, or a subset of them.
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Write the equation of the line described below in slope-intercept form.
Find the equation of the line that is perpendicular to the line y=-4 x-3 and passes through the point (10,6).
y = -1/4x + 34/4 is the equation of the line which is perpendicular to the line y = -4x - 3
Given,
The line, y = -4x - 3
Point, (x₁, y₁) = (10, 6)
We have to find the equation of line that is perpendicular to the given line;
Here,
Slope of the line, m = -1/4 (Because the line is perpendicular)
We have to find the equation line by using the formula;
y - y₁ = m(x - x₁)
Here,
y - 6 = -1/4(x - 10)
y - 6 = -1/4x + 10/4
y = -1/4x + 10/4 + 6
y = -1/4x + 34/4
That is,
The equation of the line perpendicular to the given line is y = -1/4x + 34/4
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At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis.At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping.
Relaxed time (seconds)
Jumping time (seconds)
26
21
47
40
30
28
22
21
23
25
45
43
37
35
29
32
Step 1: We need to test the given hypothesis.
We can take x1- x2 to represent the difference between the jumping and relaxed times.
[tex]H0: u1 = u2\\H1: u1 \neq u2[/tex]
Step 2: Simplification
We need to find the mean and standard deviation of both samples.
[tex]u1 = 32.375, s1 = 9.620477\\u2 = 30.625, s2 = 8.331309[/tex]
The differences between the jumping and relaxed times are calculated:
[tex]5, 7, 2, 1, -2, 2, 2, -3[/tex]
The number of differences is ∑(8, i-1) = [tex](d_{i} - \alpha ) ^{2}[/tex] = 75.5
Standard deviation differences are:
[tex]\sqrt{\frac{75.5}{7} }[/tex] = 3.284
The standard error is SE = 1.161
Using this, we can find the value of the test statistic t:
[tex]t = \frac{u1 - u2}{SE}[/tex] = 1.507
Using this and the graph, we get that the p value is 0.17554.
Therefore, since p-value is greater than α = 0.05, we cannot reject the hypothesis H0, and we can conclude that it is insufficient evidence to conclude that the average difference is not zero.
Since p-value is greater than α = 0.05, we cannot reject the hypothesis H0, and we can conclude that it is insufficient evidence to conclude that the average difference is not zero.
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A projectile is fired from ground level with an initial speed of650 m/secand an angle of elevation of 30 degrees. Use that the acceleration due to gravity is9.8 m/sec^2The range of the projectile is meters. The maximum height of the projectile is meters. The speed with which the projectile hits the ground ism/sec
The range of projectile =21556.122 m
The maximum height of the projectile will be = 5280.03 m
The speed at which the projectile hits will be 650 m/s.
Initial speed [tex]v_0=650 \:m/s[/tex]
Angle of elevation [tex]\theta=30^{\circ}[/tex]
Acceleration due to gravity [tex]=9.8 m/s^2[/tex]
i) Range of the Projectile:
[tex]$$\begin{aligned}& R=\frac{v_0^2 \sin (2 \theta)}{g}=\frac{(650)^2 \sin (30)}{9.8} \\& R=21556.122 m\end{aligned}$$[/tex]
ii) Maximum Height of the projectile.
[tex]$$\begin{aligned}& H=\frac{v_0{ }^2 \sin ^2 \theta}{2 g}=\frac{(650)^2 \sin ^2(30)}{2 \times 9.8} \\& H=5389.03 m\end{aligned}$$[/tex]
iii) The speed at which the projectile hits the ground is the same as the initial speed.
i.e. speed [tex]$=650 \mathrm{~m} / \mathrm{s}$[/tex]
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please help me solve this
I don't see the picture. Can you send it in the message.
Solve the system of linear equations
The value of x and y for the given linear equations are as follows.
For question8: x=4,y=-1
For question9 :x=-1.2, y=-(111/37)
What is linear equations?An equation in which is the highest power of to the variables 1 is knowns as the linear equation. Mathematically: it is an algebraic equations that can be also written in the form of ax + b = 0 or ax + by + c = 0, where a, b and c are definitely real numbers and x and y are variables with the highest power one.
Question 8
5x+4y=16------- eq1
-2x-4y=-4-------ea 2
5x=16-4y
X=(16-4y)/5
X=4(4-y)/5
Now substitute the value of x in equations 2
-2x-4y=-4
-2(4(4-y)/5)-4y=-4
-2(16-4y)/5-4y=-4
(-32+8y)/5-4y=-4
-32+8y-20y=-20
8y-20y= -20+32
-12y=12
y=-1
Now substitue the value of y in following equation
5x+4y=16
5x+4(-1)=16
5x-4=16
5x=4+16
x=20/5
x=4
Question 9
-5x+y=3-------------eq 1
3x-8y=24-------------eq2
-5x=-3-y
-5x= -(3+y)
x=(3+y)/5
Now substitute the value of x in equation 2
3(3+y)/5-8y=24
(9+3y)/5-8y=24
9+3y-40y=24
3y-40y=120-9
y=-(111/37)
Now substitue the value of y in following equation
-5x+y=3
-5x+(-111/37)=3
-185x-111=111
-185x=222
x= -222/185
x= -1.2
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Write an expression for the sequence of operations described below.
Subtract the quotient of 3 from h
Do not simplify any part of the expression.
Answer:
h - (3/h)
Step-by-step explanation:
The expression for the sequence of operations described is h - (3/h).
To evaluate this expression, we would first need to divide 3 by h to find the quotient, and then subtract that quotient from h. This would give us the final result of the sequence of operations.
For example, if h = 10, we would first divide 3 by 10 to get 0.3. We would then subtract 0.3 from 10 to get 9.7. This would be the final result of the sequence of operations.
In general, the expression h - (3/h) can be used to represent any sequence of operations that involves subtracting the quotient of 3 from h. The value of h can be any number, and the final result of the sequence of operations will depend on the specific value of h that is used.
Torah says he made to the development of Judaism.
Jewish Leader Action as Leader Contribution to Judaism
Abraham Start typing here..
Moses
David
Solomon
The development made to the Judaism is mentioned below;
Action as Leader;
Abraham;
Abraham's care for others is one of his leadership strengths. Abraham expressed his sorrow for Sodom and Gomorrah when the Lord informed him that they would be destroyed. He "stick his neck out for his people," as one who cares for others. He pleaded with God on their behalf.
Moses;
Early on, Moses realized he didn't have to handle everything by himself. He eventually succeeded as a leader by using delegation.
David;
As a man of God, David had learned to wait on the Lord, but he also had to learn how to be patient with those around him.
Solomon;
His name in Hebrew means peace and he used his wisdom to bring about peace in the world through deeds rather than conquest.
Contribution to Judaism
Abraham;
Before Abraham, people believed in multiple gods; Abraham was the first to preach that there is only one God. Ironically, Terach, Abraham's father, had made a fortune by selling idols of several deities.
Moses;
The Jews were delivered from slavery in Egypt by Moses, who also guided them to the Holy Land that God had promised.
David;
Many of the Old Testament Psalms are attributed to him; they were probably penned on his renowned lyre, upon which he was reputed to be a master.
Solomon;
As the Israelite monarch who constructed the first Temple in Jerusalem, Solomon is well-known. He was also the second and final king of a united Israel, which was at the height of its power during his rule (after his father, David).
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Which area on the graph, if any, represents the solution to the system?
A) A
B) B
C) C
D) No Solution
Answer:
D.) No solution
Step-by-step explanation:
Not exactly sure what the question is, not quite sure what it's asking but based on what I see on the graph, I'd say that it's D.) no solution, because both lines are parallel meaning that there is no solution to the system of equation. If there were to be a solution to the equation you would have to see an intersection which is where both lines meet/touch at a certain point. If both lines have the same point and are on top of one another that means that it has infinitely many solutions...
(If wrong, I'm sorry)
Can someone please solve a, b, c, and d? Thanks.
a) The variables are;
d = the number of hours walking his neighbor's dog.
c = the number of hours washing cars
b) The system of inequalities are;
6c + 7.5d ≥ 75
d + c ≤ 15
c) The two possible combinations are; (5, 10) and (10, 5)
d) Yes it will be sufficient
How to solve a system of equations?We are told that;
Tom is going to walk his neighbors dog for $6 an hour. Thus;
Money from walking neighbor's dog = $6 per hour
Money from car wash = $7.5 per hour
Total Number of hours of work not more than 15 hours
a) Let d represent the number of hours walking his neighbor's dog.
Let c represent the number of hours washing cars
b) Thus, money from walking neighbor's dog = 6c
Money from car wash = 7.5d
Therefore;
Total money saved = 6c + 7.5d
Since total number of hours of work is not more than 15 hours, then we have the inequality;
d + c ≤ 15
Tom needs to make at least $75 to cover prom expenses and so we have the inequality as;
6c + 7.5d ≥ 75
The system of inequalities represents this solution are;
6c + 7.5d ≥ 75
d + c ≤ 15
From the graph, the shaded part in between both lines provides the possible number of hours which we have as possibly; (5, 10) and (10, 5)
If he works 10 hours washing neighbors dogs and 3 hours on the cars, he will earn;
6(3) + 7.5(10) = $84
This is sufficient.
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