Answer:
It should take her father four hours to reach her.
Step-by-step explanation:
Since Madison takes an hour to travel 10 miles, by the time she reaches 3 hours, shes at 30 miles. (At this point her father has begun traveling towards her) And since he goes 15 miles per hour, four hours later (for her father), they will both be at the same distance.
(So in 6 hours, Madison goes 60 miles, and in 4 hours her father also goes 60 miles since hes faster)
Please tell me if I did anything wrong!
It will take the time that Madison's dad 8 hours to catch up with her.
What is Average speed?Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.
Let's call the distance from Madison's house to the point where her dad catches up with her "D".
distance Madison traveled = rate × time = 10 mph × 2 hours = 20 miles.
This means that when Madison's dad starts driving, Madison is 20 miles ahead of him.
For Madison's dad, his rate is 15 mph, and the time it takes him to catch up to Madison is "t" hours.
So his distance traveled is:
distance traveled by Madison's dad = 15 mph × t
For Madison, her rate is 10 mph, and she has already traveled for 2 hours. So her distance traveled is:
distance traveled by Madison = 10 mph × (t + 2)
Now, their distances are equal to each other:
15t = 10(t + 2) + 20
Simplifying and solving for "t", we get:
15t = 10t + 40
5t = 40
t = 8
Therefore, it will take Madison's dad 8 hours to catch up with her.
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2/3 x − 9 − 2x + 2 = 1 Which is an equivalent equation after combining like terms?
Answer:
Any equation shown in the explanation
Step-by-step explanation:
Hello!
Combining like terms means combining terms with the same variables.
So combing all x's, all y's, all numbers, etc.
2/3x - 9 - 2x + 2 = 1
combine the x's
-1 1/3 x - 9 + 2 = 1
combine normal numbers
-1 1/3 x - 7 = 1
Add 7 to both sides
-1 1/3x = 8
Make mixed number into improper fraction
-4/3x = 8
Multiply both sides by 3
-4x = 24
Divide both sides by -4
x = -6
The answer would be any of the equation I showed above
Hope this helps!
Fill in the missing values to make the equations true.
(a) log, 5 - log, 8 = log,
3
х
5
?
(b) log, I + log, 3 = log, 21
(C) log, 4 = 2log,
Step-by-step explanation:
Some of the property of log are as follows :
1. [tex]\text{log a}-\text{log b}=\text{log} \dfrac{\text{a}}{\text{b}}[/tex]
2. [tex]\text{log a}+\text{log b}=\text{log}(a{\cdot} b)[/tex]
3. [tex]\text{log}a^n=n\ \text{log} a[/tex]
Now coming to question,
(a) [tex]\text{log 5}-\text{log 8}=\text{log} \dfrac{\text{5}}{\text{8}}[/tex] (using property 1)
(b) [tex]\text{log 1}+\text{log 3}=\text{log}(1{\cdot} 3)=\text{log} 3[/tex] (using property 2)
(c) [tex]\text{log} 4=\text{log} 2^2=2\ \text{log} 2[/tex] (using property 3)
Hence, this is the required solution.
combine the like terms to create an equivalent expression : -12-6p-(-2)
Answer;
=-6p-10
Step-by-step explanation:
Lesson: It's about the using properties to simplify expression.
First, you apply by the rule.
-12-6p+2
Then, subtract by the numbers.
-12-6=-6
-6p-12+2← (group like terms)
And finally, add or subtract by the numbers.
-12+2 =-10
12-2=10
Answer: -6p-10
Hope this helps!
100 POINTS!
Convert 12 liters to barrels. (Round to 4 decimal places.)
Convert 65 ounces to liters. (There are 1000 mL in one liter.)
Round to 2 decimal places. Convert 75 minutes to days. (Round 3 decimal places.)
Step-by-step explanation:
(A) 1 L = 0.00629 barrel
12 L = 0.0755 barrel
(B) 1 ounce = 0.0296 L
65 ounces = 1.922 L
(C) 1 min = 0.000694 day
75 min = 0.05 day
Round 72.46387 to the nearest thousandth
Answer:
The answer is Zero ( 0 ).
given df with D(-1,11) and F(-9,-5) if E partitions DF such that the ratio of DE to DF is 5:8 find the coordinates of E
Answer:
(-6, 1)
Step-by-step explanation:
Since DE to DF is 5:8, we need to add 5/8 of the difference in x- and y-coordinates to the coordinates of point D to find point E.
Difference in x from D to F:
-9 - (-1) = -8
5/8 * (-8) = -5
Difference in y from D to F:
-5 - 11 = -16
5/8 * (-16) = -10
x: -1 - 5 = -6
y: 11 - 10 = 1
Answer: (-6, 1)
The coordinates are (-6, 1).
What is section formula?When a point divides a line segment externally or internally in some ratio, we use the section formula to find the coordinates of that point. It is a handy tool used to find the coordinates of the point dividing the line segment in some ratio. This section formula can also be used to find the midpoint of a line segment and for the derivation of the midpoint formula as well.
Given:
D(-1,11) and F(-9,-5)
DE : DF is 5:8
So,
DE: EF= 5 : 3
Using section formula
x= 3*(-1) + 5*(-9)/5+3
x= -3 -45 /8
x= -48/8
x= -6
and,
y= 3*11 + 5*(-5) / 8
y= 33-25/8
y= 8/8
y=1
Hence, the coordinates are (-6, 1).
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Which number produces an irrational number when added to? 3\4
Answer:
π
Step-by-step explanation:
Any other irrational number, actually, so √2 would also do the trick.
Answer:
Pi, since pi is irrational
Step-by-step explanation:
Any irrational number, such as √2
Help me please thank y’all
Answer:
45 degrees
Step-by-step explanation:
We know that angle 4 equals angle 2 because corresponding angles are congruent.
So x+30 = 2x+15,
We subtract 15 from both sides,
x + 30 - 15 = 2x + 15 - 15
x + 15 = 2x
Now we subtract x from both sides,
x - x + 15 = 2x - x
15 = x
x = 15 degrees
So we plug this in angle 4,
15 + 30 = 45 degrees
Solve the equation 8y2 – 2y - 1 = 0.
Hi there! :)
Answer:
[tex]\huge\boxed{y = -1/4, 1/2.}[/tex]
Given the equation:
8y² - 2y - 1 = 0
Find two numbers that multiply into -1 and sum up to -2. Remember, the 8 as the leading coefficient must be taken into account.
After guessing and checking, we get:
(4y + 1) (2y - 1) = 0
Use the Zero-Product Property to solve for y:
4y + 1 =
4y = -1
y = -1/4
--------------
2y - 1 = 0
2y = 1
y = 1/2
Therefore, solutions to this equation are:
y = -1/4, 1/2.
Write the series using summation notation. Then find the sum of the series.
1 + 2 + 3 + ++ + 12
And
1/2 + 1/4 + 1/6 + ++ + 1/14
Hello, please consider the following.
[tex]\displaystyle 1+2+3+...+12=\sum_{k=1}^{k=12} {k}=\dfrac{12*13}{2}=6*13=78[/tex]
For the second we will need to put on the same denominator.
[tex]\displaystyle \dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{14}=\sum_{k=1}^{k=7} {\dfrac{1}{2k}}\\\\=\dfrac{1}{2}\dfrac{420+210+140+105+84+70+60}{5*7*3*2*2}\\\\=\dfrac{1}{2}\dfrac{1089}{420}\\\\=\dfrac{1089}{840}=1.296429...[/tex]
Thank you.
Can yall help me with this one please? ✊ :(
(The problem is in the picture)
Answer:
Hey there!
Length: [tex]l\\[/tex]
Width: [tex]1/3l-1[/tex]
Expression to find the area: [tex]l(1/3l-1)[/tex], or [tex]1/3l^2-l[/tex].
Expression to find the perimeter: [tex]2l+2(1/3l-1)[/tex], or [tex]8/3l-1[/tex].
Perimeter divided by area: [tex]\frac{\frac{8}{3}l-1 }{1/3l^2-l}[/tex]
Let me know if this helps :)
Graph the function f(X)= 1n(x+4) + 5
Answer:
Graph the parent function f(x)=ln and translate all points 4 to the left and 5 up
Step-by-step explanation:
It is believed that 11% of all Americans are left-handed. A college needs to know the number of left-handed desks to place in the large instructional lecture halls being constructed on its campus. In a random sample of 140 students from that college, whether or not a student was left-handed is recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a lower percentage of left-handers than the general American population. State the random variable, population parameter, and hypotheses. State the Type I and Type II errors in the context of this problem.
Answer:
a) State the random variable
Random variable : x
which refers to a randomly selected student from the college that is left-handed.
b) state population parameter
population parameter : P
which is the percentage of all students from the college that are left handed
c) state the hypotheses
The hypothesis are;
Null hypothesis H₀ : p = 0.11
Alternative hypothesis H₁ : p > 0.11
d) State the Type I error in the context of this problem.
Type - I Error: Rejecting that the % of all the students from the college that are left-handed is 11% when actually the % is really 11%
(Reject H₀ when H₀ is true)
e) State the Type 11 error in the context of this problem
Type-II Error: Failing to Reject that the % of all the students from the college that are left-handed is 11% when the % is really higher than that
(Fail to reject H₀ when H₀ is false)
Please help me with the question that has the pink dot.
Answer:
m<FEH = 15
Step-by-step explanation:
We can find angle G
The three angles of a triangle add to 180
90 + 75+ G = 180
165 + G = 180
G = 180-165
G = 15
Since the triangles are similar, <E = <G
<E = 15
So m<FEH = 15
Answer:
m>FMH
Step-by-step explanation:
Two groups of students were tested to compare their speed working math problems. Each group was given the same problems. One group used calculators and the other group computed without calculators. Whats the hypothesis that i can test/
Answer:
Step-by-step explanation:
Two groups were tested to compare their speed at working math problems.
Aim/Objective of experiment:
To test their speed (each group and then compare) at working math problems
Control Group:
The group of students computing math problems without a calculator
Experimental Group:
The group of students computing math problems with a calculator
Statistical Hypothesis:
Null hypothesis: Both the control and the experimental group worked math problems at the same pace or speed
Alternative hypothesis: The experimental group worked math problems with a greater speed than the control group
This hypothesis is derived from the thought or knowledge that calculators help solve math problems faster. Your hope would be to refute the null hypothesis and accept the alternative hypothesis; after testing.
Find a sequence of similarity transformations
that maps AABC to ADEF. Provide the
coordinate notation for the each
transformation
Answer:
Reflect of X-axis -> diolate by a factor of 2
Remember to say thanks and mark brainliest
The sequence of similarity transformations is Reflection of Triangle ABC across the x-axis and a dilation of Triangle ABC by a scale factor of 2
What is Reflection and Dilation?
Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.
The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the triangle be ΔABC
Now , the coordinates of the triangle ABC is given as
A = A ( -4 , 2 )
B = B ( -2 , 4 )
C = C ( 0 , 2 )
And , the triangle be ΔDEF
Now , the coordinates of triangle DEF is given as
D = D ( -8 , -4 )
E = E ( -4 , -8 )
F = F ( 0 , -4 )
Now , on reflecting the triangle ABC along the x-axis , we get
The reflected triangle be A'B'C' will be the reflection of point (x, y) across the x-axis is (x, -y)
So ,
A' = A' ( -4 , -2 )
B' = B' ( -2 , -4 )
C' = C' ( 0 , -2 )
Now , on dilating the triangle A'B'C' with a scale factor of 2 , we get
D = 2 x A'
D = D ( -8 , -4 )
E = 2 x B'
E = E ( -4 , -8 )
F = 2 x C'
F = F ( 0 , -4 )
Therefore , the coordinates of the triangle DEF is
D = D ( -8 , -4 )
E = E ( -4 , -8 )
F = F ( 0 , -4 )
So , the triangle ABC is transformed into triangle DEF by a reflection across x-axis and a dilation by a scale factor of 2.
Hence , The sequence of similarity transformations is Reflection of Triangle ABC across the x-axis and a dilation of Triangle ABC by a scale factor of 2
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There are 16 entrees available at a restaurant. From these, Archie is to choose 6 for his party. How many groups of 6 entrees can he choose, assuming that the order of the entrees chosen does not matter ?
Answer: 8008
Step-by-step explanation:
Total entrees = 16
Number of entrees to choose = 6
Since order does not matter , so we combinations .
Number of combinations to choose r things out of n = [tex]C(n,r)=\dfrac{n!}{r!(n-r)!}[/tex]
Then, total ways to choose 6 entrees = [tex]C(16,6)=\dfrac{16!}{6!10!}[/tex]
[tex]=\dfrac{16\times15\times14\times13\times12\times11\times10!}{(720)10!}\\\\= 8008[/tex]
Hence, the required number of ways= 8008
the distance between the points (−5, 1) and (2, −1).
Answer:
d ≈ 7.280 units
Step-by-step explanation:
(-5, 1) & (2, -1)
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
d = √[(2 + 5)² + (-1 - 1)²]
d = √[(7²) + (-2²)
d = √(49 + 4)
d ≈ 7.280
The pipe fitting industry had 546.5 thousand jobs in 2015 and is expected to decline at an average rate of 3 thousand jobs per year from 2015 to 2025. Assuming this holds true, what will be the pipe fitting's percent change from 2015 to 2025
Answer:
The amount of jobs from fitting industry shall decline in 5.5 percent from 2015 to 2025.
Step-by-step explanation:
Due to the assumption of a yearly average rate, a linear function model shall be used. The expected amount of jobs ([tex]n[/tex]) after a certain amount of years (t) is given by the following formula:
[tex]n = n_{o} + \frac{\Delta n}{\Delta t}\cdot t[/tex]
Where:
[tex]n_{o}[/tex] - Initial amount of jobs in pipe fitting industry, measured in thousands.
[tex]\frac{\Delta n}{\Delta t}[/tex] - Average yearly rate, measured in thousands per year. (A decline is indicated by a negative sign)
If [tex]n_{o} = 546.5[/tex], [tex]t = 2025-2015 = 10\,years[/tex] and [tex]\frac{\Delta n}{\Delta t} = -3\,\frac{1}{years}[/tex], then:
[tex]n = 546.5+\left(-3\,\frac{1}{year}\right)\cdot (10\,years)[/tex]
[tex]n = 516.5[/tex]
The percent change in jobs from pipe fitting industry is calculated as follows:
[tex]\%n = \left(1-\frac{n}{n_{o}}\right)\times 100\,\%[/tex]
[tex]\% n = \left(1-\frac{516.5}{546.5}\right)\times 100\,\%[/tex]
[tex]\%n = 5.5\,\%[/tex]
The amount of jobs from fitting industry shall decline in 5.5 percent from 2015 to 2025.
PLEASE HELP! A) 5.8 B) 8.3 C) 6.2 D) 6
Answer:
x = 8.3
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj/ hyp
cos 44 = 6/x
x cos 44 / 6
x = 6/ cos 44
x=8.340981546
x = 8.3
Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. Below, enter your answers so that ∠A1 is smaller than ∠A2.)
a = 71, b = 104, ∠A = 21°
∠B1 = ∠B2 =
∠C1 = ∠C2 =
c1 = c2 =
Answer:
[tex]\angle B_{1} \approx 31.668^{\circ}[/tex], [tex]\angle B_{2} \approx 148.332^{\circ}[/tex]
[tex]\angle C_{1} \approx 127.332^{\circ}[/tex], [tex]\angle C_{2} \approx 10.668^{\circ}[/tex]
[tex]c_{1} \approx 157.532[/tex], [tex]c_{2}\approx 36.676[/tex]
Step-by-step explanation:
The Law of Sines states that:
[tex]\frac{a}{\sin A} = \frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
Where:
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Side lengths, dimensionless.
[tex]A[/tex], [tex]B[/tex], [tex]C[/tex] - Angles opposite to respective sides, dimensionless.
Given that [tex]a = 71[/tex], [tex]b = 104[/tex], [tex]\angle A = 21^{\circ}[/tex], the sine of angle B is:
[tex]\sin B = \frac{b}{a}\cdot \sin A[/tex]
[tex]\sin B = \frac{104}{71}\cdot \sin 21^{\circ}[/tex]
[tex]\sin B = 0.525[/tex]
Sine is positive between 0º and 180º, so there are two possible solutions:
[tex]\angle B_{1} \approx 31.668^{\circ}[/tex]
[tex]\angle B_{2} \approx 148.332^{\circ}[/tex]
The remaining angle is obtained from the principle that sum of internal triangles equals to 180 degrees: ([tex]\angle A = 21^{\circ}[/tex], [tex]\angle B_{1} \approx 31.668^{\circ}[/tex], [tex]\angle B_{2} \approx 148.332^{\circ}[/tex])
[tex]\angle C_{1} = 180^{\circ}-\angle A - \angle B_{1}[/tex]
[tex]\angle C_{1} = 180^{\circ}-21^{\circ}-31.668^{\circ}[/tex]
[tex]\angle C_{1} \approx 127.332^{\circ}[/tex]
[tex]\angle C_{2} = 180^{\circ}-\angle A - \angle B_{2}[/tex]
[tex]\angle C_{2} = 180^{\circ}-21^{\circ}-148.332^{\circ}[/tex]
[tex]\angle C_{2} \approx 10.668^{\circ}[/tex]
Lastly, the remaining side of the triangle is found by means of the Law of Sine: ([tex]a = 71[/tex], [tex]\angle A = 21^{\circ}[/tex], [tex]\angle C_{1} \approx 127.332^{\circ}[/tex], [tex]\angle C_{2} \approx 10.668^{\circ}[/tex])
[tex]c_{1} = a\cdot \left(\frac{\sin C_{1}}{\sin A} \right)[/tex]
[tex]c_{1} = 71\cdot \left(\frac{\sin 127.332^{\circ}}{\sin 21^{\circ}} \right)[/tex]
[tex]c_{1} \approx 157.532[/tex]
[tex]c_{2} = a\cdot \left(\frac{\sin C_{2}}{\sin A} \right)[/tex]
[tex]c_{2}= 71\cdot \left(\frac{\sin 10.668^{\circ}}{\sin 21^{\circ}} \right)[/tex]
[tex]c_{2}\approx 36.676[/tex]
The answer are presented below:
[tex]\angle B_{1} \approx 31.668^{\circ}[/tex], [tex]\angle B_{2} \approx 148.332^{\circ}[/tex]
[tex]\angle C_{1} \approx 127.332^{\circ}[/tex], [tex]\angle C_{2} \approx 10.668^{\circ}[/tex]
[tex]c_{1} \approx 157.532[/tex], [tex]c_{2}\approx 36.676[/tex]
If you want to compare two numbers and see which is greater, is it easier to use a decimal or a fraction? Group of answer choices fraction decimal
Answer:
Decimal
Step-by-step explanation:
When using decimals the bigger number is greater.
Example) .3 > .2
If there are more 0's in front of the number in a decimal it is smaller.
Example) .003 > .0003
The reason why it is harder to visualize that a fraction is greater is because there are two numbers to look at. You basically have to take an extra step and divide.
If f(x) = 2x + 2 and g(x) = x2 - 1, find (f - g)(x).
Answer:
(f - g)(x) = - x² + 2x + 3Step-by-step explanation:
f(x) = 2x + 2
g(x) = x² - 1
To find (f - g)(x) subtract g(x) from f(x)
That's
(f - g)(x) = 2x + 2 - [ x² - 1]
(f - g)(x) = 2x + 2 - x² + 1
Group like terms
That's
(f - g)(x) = - x² + 2x + 2 + 1
We have the final answer as
(f - g)(x) = - x² + 2x + 3Hope this helps you
Answer:
-x2+2x+3
Step-by-step explanation:
(2x+2)- (x2-1)
2x+2-x2+1
-x2+2x+3
Can u help me on the mystery sequence hidden in the dominoes
Answer: 80
Step-by-step explanation:
A) The first domino is 3, the second is 4. Hence 34.
B) The first domino is 5, the second is 1. Hence 51.
C) The first domino is 6, the second is 11. Hence 71.
D) The first domino is 7, the second is 10. Hence 80.
What is the domain in the equation y=x+1?
Answer:
all real numbers
Step-by-step explanation:
The domain of any polynomial function is "all real numbers." There is no value of x for which y is undefined.
Given the following probability distribution, what is the expected value of the random variable X? X P(X) 100 .10 150 .20 200 .30 250 .30 300 .10 Sum1.00 Multiple Choice 175 150 200 205
Answer:
d) 205
Step-by-step explanation:
Step(i):-
x : 100 150 200 250 300
p(X=x) : 0.10 0.20 0.30 0.30 0.10
Step(ii):-
Let 'X' be the discrete random variable
Expected value of the random variable
E(X) = ∑ x P(X=x)
= 100 X 0.10 + 150 X 0.20 + 200 X 0.30 +250 X 0.30 + 300 X 0.10
= 205
Final answer:-
The expected value E(X) = 205
A motorcycle travels 360km. What is it's average speed in km/hr?
Answer:
60km/hr
Step-by-step explanation:
considering it travels for 6 hours
360 divided by 6= 60km/hr
4-7 please help BRAINLEST
Answer:
n = 12
Step-by-step explanation:
27 = 15 + n
27 - 15 = n
12 = n
Answer:
n= 12
Step-by-step explanation:
27=15+n
15+n=27
n=27-15
n=12
I(t) models the daily solar irradiance, measured in kWh/m2-day on a farm, t days after the summer solstice. Here, t is entered in radians. I(t) = 1.5cos(2π/365*t)+4.3 What is the second time after the summer solstice that the solar irradiance is 5.2kWh/m2-day Round your final answer to the nearest whole day.
Answer:
311 days
Step-by-step explanation:
I(t) = 1.5 cos(2π/365 t) + 4.3
5.2 = 1.5 cos(2π/365 t) + 4.3
0.9 = 1.5 cos(2π/365 t)
0.6 = cos(2π/365 t)
2π/365 t = cos⁻¹(0.6)
2π/365 t = 0.927, 5.356
t ≈ 54, 311
Answer:
First time is 54
Second time is 311
Step-by-step explanation:
You plug in the numbers to get the answer.
cos⁻¹(0.6) = 2π/365t
0.927, 5.356 = 2π/365t
t = 54 or 311
Please help willl give 5 stars!
Answer:
9. 6, 2, -2,-6,-10,-14
Step-by-step explanation: