Answer:
C:2 gallons per minute
Step-by-step explanation:
Answer:
The answer is two gallons per minute.
Step-by-step explanation:
The gallons are always double the minutes. This means that there are 2 gallons per minute.
Convert to find the equivalent rate.
960 packages per
hour
packages per
week
Answer:
161,280 packages in 1 week
Step-by-step explanation:
there are 168 hours in 1 week
so 960 × 168 = 161,280
The fifth term of a non liner sequence is 324.The term to term rule is multiply 3
Work out the second term of the sequence
Answer:
324 642
Step-by-step explanation:
A college graduate is curious about the proportion of graduates who have loan debt 20 years after graduating. Let the proportion of graduates who have loan debt 20 years after graduating be p. If the college graduate wishes to know if the proportion of graduates who have loan debt 20 years after graduating is less than 18%, what are the null and alternative hypotheses?
Select the correct answer below:
H0: p=0.18; Ha: p<0.18
H0: μ=0.18; Ha: μ<0.18
H0: p=0.18; Ha: p>0.18
H0: p<0.18; Ha: p=0.18
The correct null and alternative hypotheses in this case are:H0: p >= 0.18 (the proportion of graduates with loan debt 20 years after graduating is greater than or equal to 18%)
Ha: p < 0.18 (the proportion of graduates with loan debt 20 years after graduating is less than 18%)
Here, the null hypothesis assumes that the proportion of graduates with loan debt 20 years after graduating is greater than or equal to 18%. The alternative hypothesis assumes that the proportion of graduates with loan debt 20 years after graduating is less than 18%, which is what the college graduate wishes to test. Therefore, if the sample data provides sufficient evidence to reject the null hypothesis, then it can be concluded that the proportion of graduates with loan debt 20 years after graduating is less than 18%.
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Given the system of equations: 5x + 2y = 3 4x − 8y = 12 solve for (x, y) using elimination.a. (−7, 5) b. (−5, −4) c. (1, −1) d. (3, −6)
(x,y) = (1, -1). Option (c) is the correct answer.
Given equations:
5x + 2y = 3 ..(1)
4x - 8y = 12 ..(2)
Solving using the elimination method:
so, 4x = 8y + 12 or x = 2y + 3 ..(3)
Now, substituting the x in equation(1) from equation(3)
so we get,
5(2y+3) + 2y = 3
10y + 15 + 2y = 3
12y = -12
y = -1
Putting the value of y in equation(3)
x = 2(-1) + 3 = 1
x = 1
Therefore, (x,y) = (1, -1)
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Answer: Option C, (-1,1)
Step-by-step explanation:
What is the angle relationship between angles 2 and 6? Please help, thanks!
Answer:
Corresponding and Congruent
Step-by-step explanation:
Find the discriminant and use it to describe the type of solutions x^2-7x+3=0
Answer:
D = 36
Since the discriminant is greater than zero, hence the root of the equation will be real and distinct
Step-by-step explanation:
Find the discriminant and use it to describe the type of solutions x^2-7x+3=0
Given the quadratic equation
ax²+bx+c = 0
Discriminant is expressed as
D = b² - 4ac
It is used to determine the nature of the roots of the equation
Given the equation x^2-7x+3=0'
a = 1, b = -7 and c = 3
D = (-7)² - 4(1)(3)
D = 49 - 12
D = 36
Since the discriminant is greater than zero, hence the root of the equation will be real and distinct
6. Salary Raise. A Union negotiates for a cost-of-living raise of 3.4%. What is the raise for a union
member whose salary is $42,360. What is this person's new salary? D5
(1 Punto)
Answer:
New salary= $43,800.24Step-by-step explanation:
Step one:
Given data
the initial salary is = $42,360
the raise in percentage is =3.4%
To know the raise we need to calculate what the amount of 3.4% of $42,360 is
Step two:
=(3.4/100)*42,360
=0.034*42360
=1440.24
therefore thr raise is $1440.24
Step three:
the new salary is given as
new salary= old salary+ raise
New salary= $42,360+$1440.24
New salary= $43,800.24
Plzzzz help fast !!
One month Chris Rented 3 movies and 2 video games for a total of $15 . the next month he rented 8 movies and 4 video games for a total of $33. find the rental cost for each movie and each video game
Answer:
Both are a total of $3
Step-by-step explanation:
Because if you add 3+2= 5 and then you divided; 15÷5= 3, then you add 8+4=12, and you do the same like the other; 33÷12= 2.75 and if you round it, the answer will be 3.
So in conclusion both the movies and the video games are $3
PLEASE HELP WITH THIS WILL GIVE BRINALIST TO BEST ASNWER
What are the 2 different elastic forces? Explain how each will return their object back to their object back to their original shape.
There are two types of elastic forces- compression and tension.Something that is elastic can return to its original shape after being stretched or compressed. tension- The energy is stored until the force is removed and the object springs back to its original shape, doing work in the process
Which expression is equivalent to V-80?
-455
O -4.5;
O 4.5;
O 415
Answer:
4.5;this i guess it will be
The expression is equivalent to √-80 is 4√5i
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is an expression √-80, we need to find an expression is equivalent to it.
√-80
Since, √-1 = i
Therefore,
we can write,
√-80 = √-1×80
= √80×√-1
= √80×i
= √80i
= √16×5i [∵ 80 = 16 ×5]
= 4√5i [∵ √16 = 4]
Hence, the expression is equivalent to √-80 is 4√5i
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The complete question is attached
what is the slope of this graph?
Answer:
1/2
Step-by-step explanation:
I got the answer right on the test
(X2 + 2x - 1) + (x3 - 2x + 1)
What is the recursive rule for the following arithmetic sequence?
-7, -4, -1, 2, 5, …
Answer:
Recursive rule for arithmetic sequence = an = a[n-1] + 3
Step-by-step explanation:
Given arithmetic sequence;
-7, -4, -1, 2, 5, …
Find:
Recursive rule for arithmetic sequence;
Computation:
Let a1 = -7
So,
⇒ a2 = a1 + 3 = -4
⇒ a3 = a2 + 3 = -1
⇒ a4 = a3 + 3 = 2
⇒ a5 = a4 + 3 = 5
So, the recursive formula is
⇒ an = a[n-1] + 3
Recursive rule for arithmetic sequence = an = a[n-1] + 3
Chelsea is budgeting for her trip to the mall. She
does not want to spend any more than $140. If
she wants to buy a dress that costs $28.50 and
I some shirts that cost $20.75 each, how many
shirts can she buy? Use the inequality to help
solve the problem.
140 > 28.50 + 20.75x
Answer:
Chelsea can buy 5 shirts.
Step-by-step explanation:
Subtract 28.50 from 140. This is because subtraction is the inverse of addition, so it will cancel out. 111.50 > 20.75xDivide both sides by 20.75. Division is the inverse of multiplication. 5.3734939759 > xYou can't split shirts when buying them, so Chelsea can buy 5 shirts.
A person runs 1/2 miles in 1/16 hour
Answer:
He runs a mile in 1/8 of an hour
he can run 8 miles in one hour
Step-by-step explanation:
h(x)=6x Find x if h(x) = -12
a•8
b•28
c•-2
d•-1
a tank contains 150 liters of fluid in which 20 grams of salt is dissolved. brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 3 l/min; the well-mixed solution is pumped out at the same rate. find the number a(t) of grams of salt in the tank at time t.
The initial amount of salt is 20 grams and the rate of change is equal to the difference between the rate at which salt enters the tank and the rate at which it leaves. This is expressed by the equation a'(t) = 1 - (a(t)/150)*3, where a'(t) is the derivative of a(t) with respect to time.
The function a(t) is given by a differential equation, which describes the rate of change of the amount of salt in the tank with respect to time.
To solve the differential equation, we can use separation of variables and integrate both sides with respect to t.
This gives us
ln|a(t)-50| = -3/50*t + C, where C is a constant of integration. Solving for a(t), we get
\(a(t) = 50 + Ce^(-3/50*t).\)
Using the initial condition a(0) = 20, we can solve for the constant C, which is C = -30.
Therefore, the function a(t) is \(a(t) = 50 - 30e^(-3/50*t).\). The function tells us the number of grams of salt in the tank at any given time t.
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If Samantha can make 6 bracelets in 1 hour and Payton makes 15 bracelets in 3 hours - what is the difference in the number of
bracelets they would make in 6 hours?
Find the value of Y0 for which the solution of the initial value problem y′−2=8 + 9sint, y(0)=y0 remains finite as t→infinity.
The value of Y0 for which the solution of the initial value problem y′−2=8 + 9sint, y(0)=y0 remains finite as to infinity is -5/2.
What is the initial value?In mathematics, the y-intercept of a function is indicated by the beginning value of the function. Understanding the y-intercept is beneficial for graph functions.
Employ the first-order linear differential equation's solution formula, which I've lately demonstrated numerous times here.
\(y = e^t[e^{-t}(1+3sin(t)) dt + c] = -(\frac{1}{2})(3sin(t) + 3cos(t) + 2) + ce^t\)
After doing integration by parts twice.
Since lim{t->oo} y is finite, c = 0.
So, y(0) = -(1/2)(3+2) = -5/2
Therefore, the value of Y0 for which the solution is -5/2.
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Angle relationships with parallel lines can someone answer please help
Answer:
x°= 34°
m<x and angle measuring 34° are corresponding angles since two lines are parallel with a third line intersecting them.
Write an equation for the graph below in terms of x
Answer:
Y = -x - 1
Step-by-step explanation:
Slope (rise / run) is -1 and the y-intercept is -1.
Hoep this helps. Pls give brainliest.
Equation for the graph below in terms of x is
\(y=-1x-1\)
Given :
The graph of a line . we need to write equation for the line graph
'Equation of a line is in the form of \(y=mx+b\)
where m is the slope and b is the y intercept
y intercept is the point where the graph crosses y axis
The graph crosses y axis at -1
so y intercept \(b=-1\)
Now we find out slope . Lets pick two points from the graph
\((-1,0) and (0,-1)\\slope(m)=\frac{y_2-y_1}{x_2-x_1} =\frac{-1+0}{0+1}=-1\)
slope m=-1 and b=-1
Substitute the slope and y intercept in y=mx+b
Equation for the graph below is
\(y=-1x-1\)
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Simplify
(sec ∅ - 1)(sec ∅+ 1)
Answer:
\(tan^2(x)\)
Step-by-step explanation:
\((sec(x)-1)(sec(x)+1)\\sec^2(x) - 1\\\frac{1}{cos^2(x)} -1\\\frac{1-cos^2(x)}{cos^2(x)} \\\frac{sin^2(x)}{cos^2(x)}\\ \\tan^2(x)\)
three construction companies have bid for a job. max knows that the two companies with which he is competing have probabilities 1/7 and 1/4, respectively, of getting the job. what is the probability that max will get the job? (enter your probability as a fraction.)
The probability that Max will get the job is 17/28 or approximately 0.61. This is calculated by subtracting the sum of the probabilities of the other two companies getting the job from 1.
To calculate the probability that Max's construction company will get the job, we first need to understand that the sum of probabilities for all three companies must equal 1. Let the probability of Max's company getting the job be represented by P(Max).
Since the probabilities of the two competing companies are 1/7 and 1/4, we can write the equation:
P(Max) + 1/7 + 1/4 = 1
To solve for P(Max), we first need to find a common denominator for the fractions. The least common denominator for 7 and 4 is 28. So, we can rewrite the equation as:
P(Max) + 4/28 + 7/28 = 1
Now, we can combine the fractions:
P(Max) + 11/28 = 1
To find P(Max), we subtract 11/28 from 1:
P(Max) = 1 - 11/28
Since 1 is equal to 28/28, the equation becomes:
P(Max) = 28/28 - 11/28
Now, we subtract the fractions:
P(Max) = 17/28
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Elena is thinking through a proof using a reflection to show that the base
angles of an isosceles triangle are congruent. Complete the missing
information for her proof.
B
Construct the perpendicular
bisector of segment CD. The perpendicular bisector of CD must go through B
since it's the midpoint. A is also on the perpendicular of CD because the
Call the midpoint of segment CD
distance from A to
We want to show triangle ADC is congruent to triangle ACD. Reflect triangle
ADC across line
is the same as the distance from A to
Since
is on the line of reflection, it
definitely lines up with itself. DB is congruent to
perpendicular bisector of CD. D' will coincide with
other side of a perpendicular line and the same distance from it (and that's
the definition of reflection!). C" will coincide with;
other side of a perpendicular line and the same distance from it (and that's
the definition of reflection!). Since the rigid transformation will take triangle
ADC onto triangle ACD, that means angle
therefore they are congruent.
since AB is the
since it is on the
since it is on the
will be taken onto angle
(they are corresponding parts under the same reflection), and
Answer:
The missing information for the proof is:
- Point D' will coincide with point D, since it is on the perpendicular bisector of CD and the same distance from it (and that's the definition of reflection!).
- Point C" will coincide with point C, since it is on the perpendicular bisector of CD and the same distance from it (and that's the definition of reflection!).
- Angle ADC will be taken onto angle ACD, since they are corresponding parts under the same reflection. Therefore, they are congruent.
If I1 ⊇ I2 ⊇ .... In ⊇... is a nested sequence of intervals and if In = [an; bn], show that a1 ≤ a2 ≤ ....... ≤ an ≤ ........ and b1 ≤ b2 ≤..... bn ≤ ......
The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:
1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.
To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.
First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.
Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.
We can continue this process for all the intervals in the sequence, until we reach In. So we have:
a1 ≤ a2 ≤ ... ≤ an-1 ≤ an
and
b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn
This shows that the endpoints of the intervals are ordered in the same way.
Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:
Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:
1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.
Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .
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Find the measures of the angles of a triangle if the measure of one angle is twice the measure of a second angle and the third angle measures 3 times the second angle decreased by 48.
Answer:
38°, 66° and 76°Step-by-step explanation:
A triangle consists of 3 angles and sides. The sum of the angles in a triangle is 180°. Let the angle be <A, <B and <C.
<A + <B + <C = 180° ...... 1
If the measure of one angle is twice the measure of a second angle then
<A = 2<B ...... 2
Also if the third angle measures 3 times the second angle decreased by 48, this is expressed as <C = 3<B-48............ 3
Substituting equations 2 and 3 into 1 will give;
(2<B) + <B + (3<B-48) = 180°
6<B- 48 = 180°
add 48 to both sides
6<B-48+48 = 180+48
6<B = 228
<B = 228/6
<B =38°
To get the other angles of the triangle;
Since <A = 2<B from equation 2;
<A = 2(38)
<A = 76°
Also <C = 3<B-48 from equation 3;
<C = 3(38)-48
<C = 114-48
<C = 66°
Hence the measures of the angles of the triangle are 38°, 66° and 76°
If p is the hypothesis of a conditional statement and q is the conclusion, which is represented by q→p?
O the original conditional statement
O the inverse of the original conditional statement
O the converse of the original conditional statement
O the contrapositive of the original conditional statement
Answer:
(c) the converse of the original conditional statement
Step-by-step explanation:
If a conditional statement is described by p→q, you want to know what is represented by q→p.
Conditional variationsFor the conditional p→q, the variations are ...
converse: q→pinverse: p'→q'contrapositive: q'→p'As you can see from this list, ...
the converse of the original conditional statement is represented by q→p, matching choice C.
__
Additional comment
If the conditional statement is true, the contrapositive is always true. The inverse and converse may or may not be true.
<95141404393>
Can someone please help me
The proof that show show how ΔTRS ≅ ΔQRP by SAS congruence theorem is explained below.
What is the SAS Congruence Theorem?The SAS congruence theorem states that if two triangles have one pair of corresponding included angles that are congruent, and two pairs of corresponding sides that are also congruent, then both triangles are congruent to each other.
Using the SAS, the proof that shows both triangles are congruent is explained below.
Statements Reasons
1. SR ≅ PR 1. Given
2. SP bisects TQ 2. Given
3. TR ≅ QR 3. Definition of bisection
4. ∠TRS ≅ ∠QRP 4. Vertical ∠s theorem
5. ΔTRS ≅ ΔQRP 5. SAS congruence theorem
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what is 20 minutes past 8
Answer:
8:20
Step-by-step explanation:
you just ads 20 minutes to 8:00
The equation of a circle is given below.
x^{2}+(y+4)^{2} = 64x
2
+(y+4)
2
=64x, squared, plus, left parenthesis, y, plus, 4, right parenthesis, squared, equals, 64
What is its center?
((left parenthesis
,,comma
))right parenthesis
What is its radius?
If necessary, round your answer to two decimal places.
units
Answer:
(h,k) = (32,-4)
r = 32
Step-by-step explanation:
The general equation for a circle is given by:
\((x-h)^2+(y-k)^2=r^2\) (1)
where (h,k) is the center of the circle and r is the radius.
You have the following equation:
\(x^2+(y+4)^2=64x\) (2)
You first need to complete squares in order to obtain an equation of the form (1). Thus, you have that the second term must be in a perfect square trinomial:
2b = 64
b = 32
Then, you have to sum 32^2 and also subtract the same number in the expression (2):
\(x^2-64x+(y+4)^2=0\\\\(x^2-64x+32^2)+(y+4)^2-32^2=0\\\\(x-32)^2+(y+4)^2=32^2\)
you compare the last result with expression (1) and obtain that the raiuds of the circle is r = 32
Furthermore, the center of the circle is (h,k) = (32,-4)