Answer:
The null hypothesis is [tex]H_0: \mu = 14[/tex]
The alternate hypothesis is [tex]H_a: \mu < 14[/tex]
The test statistic is t = -1.95.
The p-value is of 0.0292. This means that for a level of significance of 0.0292 and higher, there is sufficient evidence to conclude that the highlighters wrote for less than 14 continuous hours.
Step-by-step explanation:
Suppose a consumer product researcher wanted to find out whether a highlighter lasted less than the manufacturer's claim that their highlighters could write continuously for 14 hours.
At the null hypothesis, we test if the mean is 14 hours, that is:
[tex]H_0: \mu = 14[/tex]
At the alternate hypothesis, we test if the mean is less than 14 hours, that is:
[tex]H_a: \mu < 14[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
14 is tested at the null hypothesis:
This means that [tex]\mu = 14[/tex]
X = 13.6 hours, s = 1.3 hours. Sample of 40:
In addition to the values of X and s given, we have that [tex]n = 40[/tex]
Test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{13.6 - 14}{\frac{1.3}{\sqrt{40}}}[/tex]
[tex]t = -1.95[/tex]
The test statistic is t = -1.95.
P-value:
The p-value of the test is the probability of finding a sample mean lower than 13.6, which is a left tailed test, with t = -1.95 and 40 - 1 = 39 degrees of freedom.
Using a calculator, the p-value is of 0.0292. This means that for a level of significance of 0.0292 and higher, there is sufficient evidence to conclude that the highlighters wrote for less than 14 continuous hours.
EX 2
QUAD ABCD is a rectangle with
diagonals that intersect at point P.
AC = 4x-13 and DP = x + 7. Find the
value of 'x'.
QUAD ABCD is a rectangular shape whose diagonals meet at point P. AC is 4x-13 and DP is x + 7.
Can you show that the quadrilateral ABCD is a parallelogram given the provided information?When one set of opposing sides in a quadrilateral are congruent and parallel, the quadrilateral is a parallelogram. ABCD is a parallelogram if — BC — AD and — BC — AD. A quadrilateral becomes a parallelogram if its diagonals are bisected by one another.
In QUAD ABCD, DP equals x + 7 and AC is 4x-13.
4x - 13 is x + 7 + x + 7
4x - 13 = 2x+14
2x-13 = 14.
hence,
The value of x is 13.5.
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If P(7,5) and P'(2,8), then the rule for translation is T(x,y)=(x-?, y+?).
Answer:
Step-by-step explanation:
Answer: x is -5 and y is +3
Step-by-step explanation:
yes
assuming all parabolas are of the form y = ax^2 + bx + c drag and drop the graphs to match the appropriate a-value
Answer:
A parabola has the form:
y = a*x^2 + b*x + c
Where a is the leading coefficient.
If a is positive, the parabola opens up.
If a is negative, the parabola opens down.
a is the factor that multiplies the part that grows the fastest in the equation, thus, if a is a larger value (in absolute value) then the parabola will grow faster (then the parabola will be narrow)
if a is smaller (again, in absolute value) the parabola will grow slower, then the parabola will be wider.
With this, we can conclude that:
a = -4
is the largest value of a in absolute value.
Then this corresponds to the thinner parabola (the one at the left)
a = -1
Is the middle value of a, then this corresponds to the graph of the middle
a = -0.25
Is the smallest absolute value of a, then this one corresponds to the widest graph (the first one at the left)
Choose the values of a and b that represent the factored form of w2 – 11w + 18.
w2 – 11w + 18 = (w – a)(w – b)
a =
b =
a = 2
b = 9
........................
Answer:
a=2 b=9
Step-by-step explanation:
w^2-11w+18=0
w^2-9w-2w+18=0
w(w-9)-2(w-9)=0
w=2 or w=9
Therefore a=2 and b=9
Target offers a discount if you spend at least $50. Write an inequality to represent d, how much you must spend to receive the discount.
Answer:
d ≥ 50
Step-by-step explanation:
To receive the discount, you must spend at least $50, which can be represented by the inequality d ≥ 50. This inequality means that the amount you must spend (d) is greater than or equal to $50. If you spend more than $50, you will receive the discount. If you spend less than $50, you will not receive the discount.
ILL BRAINLIEST YOU PLEASE HELP ME
i don't know the answer to this question, but i can give you an example that way you can find your own answer!
possible answers for the example question:
65∘
115∘
35∘
75∘
85∘
To find the measure of angle DAC, we must know that the interior angles of all triangles sum up to 180 degrees. Also, as this is an isosceles trapezoid, ∠ADC and ∠BCD are equal to each other. The two diagonals within the trapezoid bisect angles ∠ADC and ∠BCD at the same angle.
Thus, ∠ACD must also be equal to 50 degrees.
Thus, ∠ADC=50+15=65.
Now that we know two angles out of the three in the triangle on the left, we can subtract them from 180 degrees to find ∠DAC:
180−65−50=65
the correct answer for the example question is 65 degrees
Choose the right one.
Answer:
Skewed Right
Step-by-step explanation:
Took the test
Answer:
C
Step-by-step explanation:
what is the equation of a line that is parallel to 4x+3y=12 AND passes through the point (3,4) ?
Answer:
Step-by-step explanation:
Given Line equation is 4x+3y=12 and point (3,4)
Given condition two line are parallel
Parallel means two straight lines having same slope.
From the above condition we can use "point-slope" equation.
[tex]y-y_{1} =m(x-x_{1} )[/tex]
From the given line equation we can find slope easily.
We can rewrite the line equation as [tex]y=-\frac{4}{3} x+4[/tex]
We can compare the above equation as y=mx+b
slope [tex]m=-\frac{4}{3}[/tex] and point [tex](x_{1} ,y_{1} )[/tex]=(3,4) submit in slope-point equation.
Becareful while submit point in the slope point equation.
Note:(Many students do mistakes while submitting point.
[tex]y-4=-\frac{4}{3}(x-3)[/tex]
solve and get the answer
Equation of line is 4x+3y=24
A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points negative one, zero and zero, one. A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points negative one, zero and zero, one. What is the slope of the line?
The slope of the line on the given coordinate plane is equal to 1.
How to calculate the slope of a line?In Mathematics, the slope of a straight line can be calculated by using this this mathematical expression;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
From the information provided in the graph, we have the following data points on the line:
Points on x-axis = (-1, 0).
Points on y-axis = (0, 1).
Substituting the given points into the slope formula, we have the following;
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (1 - 0)/(0 - (-1))
Slope, m = 1/(0 + 1)
Slope, m = 1/1
Slope, m = 1
In conclusion, we can logically deduce that the slope of this line is equal to 1.
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HELP DUE IN 15 MINS!
Find the measures of the numbered angles in the parallelogram.
m∠1 =?? degrees
° m∠2 =?? degrees
° m∠3 =?? degrees
Answer:
m∠1 = 25° (opposite angles are congruent)
m∠2 = 87° ⇒ 180 - (25 + 68)
m∠3 = 68° ⇒ 180 - (87 + 25)
Hope this helps!
At an arts festival, Jamal, a camp counselor, bought food tickets for his hungry campers. The campers can use them to get hot dogs, which cost 4 tickets apiece, and burgers, which cost 5 tickets apiece. In total, the campers can use up to 21 tickets, which is how many Jamal bought. Write an Inequality that best describe this situation
Inequality in its most basic form explains this circumstance is 5x + 4y ≤ 21
What isan Inequality?Jamal, a camp counsellor, purchased meal tickets at an arts festival for his ravenous kids. The campers may use them to purchase burgers and hot dogs, both of which cost four tickets each.
A camp counsellor purchased meal tickets at an arts festival for her ravenous kids.
The campers may use them to purchase burgers and hot dogs, both of which cost four tickets each.
Let x be the number of hot dogs and y be the number of burgers. In all, campers are allowed to utilise up to 21 tickets.
Thus, inequality in its most basic form explains this circumstance.
= 5x + 4y ≤ 21
Inequality in its most basic form explains this circumstance is 5x + 4y ≤ 21
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The net best represents which of the solids?
Answer:
Where is the picture for the question?
A painting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. The painting was enlarged by 10%. By what percent is the new frame bigger than the original frame if the width of the frame remains the same?
PLEASE HELP
The percent that the new frame is bigger than the original frame if the width of the frame remains the same is 9.1%.
How to illustrate the percentage?From the information, the painting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. The painting was enlarged by 10%.
Let the length be Illustrated as 10cm.
Width = 10% × 10cm
= 1cm
New Length = 10cm + (10% × 10cm)
= 11cm
The old perimeter will be:
= 2(1 + 10)
= 22cm
New perimeter will be:
= 2(1 + 11)
= 24cm
The percentage increase will be:
= (24 - 22) / 22 × 100
= 2/22 × 100
= 9.1%
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What is the name of a 3 4 5 triangle?
The right angle triangle is the name of the 3, 4, and 5 triangles.
A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle.
The formula states that in a right triangle:
The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.
(Hypotenuse)² = (Base)² + (Altitude)²
c²=a²+b²
The three numbers which satisfy the above formula are the Pythagorean triplets
Properties of right angle:
The largest angle is always 90º and called the hypotenuse which is always the side opposite to the right angle.
The measurements of the sides follow the Pythagoras rule, which cannot have any obtuse angle.
consider c=5 a=3, b=4 substitute in above formula:
5²=3²+4²
⇒25=9+16
⇒25=25
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Question is in the photo below
Answer:
A
Step-by-step explanation:
mark me brainliest pls
Answer:
A. 24
Step-by-step explanation:
The angle formed by two secants intersecting outside of a circle is equal to half of the difference of the intercepted arcs.
In other words, ∠1 is 104 minus 56, divided by 2.
[tex]\frac{104-56}{2} =\frac{48}{2}= 24[/tex]
Jaimie ran 3 1/2 on Monday. She ran half
as far on Tuesday as she did on Monday. How
far did Jaimie run in all on Monday and
Tuesday?
Answer: So Jamie ran 3 1/2 miles on Monday and half that distance on Tuesday. We need to know how far she ran "in all" which are key words for "addition".
We need to add 3 1/2 + (1/2)(3 1/2)
It's probably easiest to do this by converting to an improper fraction.
So let's convert:
3 1/2 is the same as 7/2. now we can rewrite the problem:
7/2 + (1/2)(7/2)
= 7/2 + 7/4 . Now we need a common denominator:
7/2 = 14/4
Now we have 14/4 + 7/4 = 21/4. Now we should convert to a mixed number.
21/4 = 5 1/4
So Jamie ran 5 1/4 miles in all.
Step-by-step explanation:
Answer:
5.25 or 5 1/4 (Whichever you prefer)
Step-by-step explanation:
To make it simpler, we will convert 3 1/2 to decimal format.
First, take 3 and multiply it by the denominator 2 of 1/2, then add that number to the numerator of 1/2
3 x 2=6 -> 6+1=7
now add the denominator 2 under 7 and we now have 7/2, the equivalent to the mixed number 3 1/2
Afterward, to get the decimal, divide the numerator by the denominator:
7 divided by 2= 3.5
Now halve 3.5 to get the number Jaimie ran on Tuesday -> 1.75
Then add both 3.5 (3 1/2) and 1.75 (1 3/4), to get 5.25 or 5 1/4, which is your answer.
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Which of the following lists is in order from least to greatest?
3 × 10 -2, 4 -1, , |-2|
|-2|, 4 -1, , 3 × 10 -2
, 3 × 10 -2, |-2|, 4 -1
4 -1, 3 × 10 -2, |-2|,
Answer: Order from Least to Greatest
-1/8 < 0.33 < 3/8 < 75% < 1 5/8
Step-by-step explanation:
To compare and order fractions we must first convert all integers, mixed numbers (mixed fractions) and fractions into values that we can compare. We do this by first converting all terms into fractions, finding the least common denominator (LCD), then rewriting each term as an equivalent fraction with the LCD. Then we compare the numerators of each fraction and put them in correct order from least to greatest or greatest to least.
Answer:
a
Step-by-step explanation:
hi this is the kid u talked to during aprill and may about that game little alchemy.
Help
There were 16 bald eagles in an
area. Some years later, there
were 28 bald eagles in the area.
What is the percent gain?
[? ]%
Answer:
75%
Step-by-step explanation:
16 increases by 75 percent in order to reach 28.
How many solutions does the system in the image shown
A:one solution
B:zero solutions
C:infinitely many solutions
Answer:
c
Step-by-step explanation:
Please help with this I really mean it because if its wrong I fail
Answer:
16 is the correct answer
Stella is running a bakery. She has made a street sign to direct people to her bakery. She painted one side of the post and sign. What is the painted area. 75, 8, 12, 12, 4 1. 11 2. 13 3. 21 4. 4
Answer:
768 square inches
Step-by-step explanation:
Area of the rectangle = length × width
Length = 75 in
Width = 12 in
Area of the rectangle = length × width
= 75 in x 8 in
= 600 in²
Area of the square = length ²
Length = 12 in
Area of the square = length ²
= 12 in²
= 12 in × 12 in
= 144 in²
Area of a triangle = 1/2bh
b = base = 12 in
h = height = 4 in
Area of a triangle = 1/2bh
= 1/2 * 12 in * 4 in
= (1*12*4)in² / 2
= 48 in² / 2
= 24 in²
Total area of the painted part of the street sign = Area of the rectangle + Area of the square + Area of a triangle
= 600 in² + 144 in² + 24 in²
= 768 in²
Kate is putting mulch down in her circular shaped garden. The garden has a radius of 12 feet. How much mulch does she need?
Kate needs to buy 453.6 ft2 of mulch for her 12 ft radius garden, which is equal to 76.3 cubic feet when multiplied by the desired depth.
Kate needs to purchase 453.6 cubic feet of mulch for her garden. To figure this out, she needs to first calculate the area of her garden using the formula A = πr2, where A is the area of the garden and r is the radius. In this case, the area of Kate’s garden is 453.6 ft2. For example, if she wants to put down 2 inches of mulch, she would need to purchase 453.6 ft2 x 0.167 ft = 76.3 cubic feet. This calculation can be adjusted depending on the depth of mulch desired. For example, if Kate wants to put down 3 inches of mulch, she would need to purchase
453.6 ft2 x 0.25 ft = 113.4 cubic feet
A = πr2
A = π(12)2
A = 453.6 ft2
Mulch = A x depth
Mulch = 453.6 ft2 x 0.167 ft
Mulch = 76.3 cubic feet
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Help with math question please
what are the coordinates of the center of the center and the length of the radius of the circle whose equation is x^2 y^2
The coordinates of the center of the circle and the radius length of the specified circle are (-3,2) and 6 units, respectively.
What is circle?A circle is a shape formed by all points in a plane that are at a particular distance from the center. It is the curve sketched out by a point moving in a plane so that its distance from a particular point remains constant. A circle is a closed two-dimensional object in which the set of all the points in the plane is equidistant from a particular point called "centre". The line of reflection symmetry is formed by every line that travels through the circle. It also features rotational symmetry around the center for all angles.
Here,
x²+6x+9-9+y²-4y+4-4=23
(x+3)²-9+(y-2)²-4=23
(x+3)²+(y-2)²=36
(x+3)²+(y-2)²=6²
center=(-3,2)
radius=6
The coordinates of the center of the center and the length of the radius of the given circle is (-3,2) and 6 units.
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*****50 POINTSSSS*****
In the figure, quadrilateral GERA is inscribed in circle P. Line TA is tangent to circle P at A, m∠REG = 78°, the measure of arc AR = 46°, and segment ER ≅ segment GA. Find each of the following measures.
m∠GAR =
m∠TAR =
measure of arc GE =
measure of arc AG =
m∠GAN =
measure of arc RE =
Answer:
Givenm∠REG = 78°mAR = 46°ER ≅ GASolutionm∠GAR = 180° - m∠REG = 180° - 78° = 102° (supplementary angles sum to 180°)m∠TAR = 1/2mAR = 1/2(46°) = 23° (tangent chord angle is half the size of intercepted arc)m∠GAN = 180° - (m∠TAR + m∠GAR) = 180° - (23° + 102°) = 55° (straight angle is 180°)mAG = 2m∠GAN = 2(55°) = 110°mRE = mAG = 110° (as ER ≅ GA)mGE = 360° - (mAG + mAR + mRE) = 360° - (110° + 46° + 110°) = 94° (full circle is 360°)1. A taxi charges a flat rate of $1.75 plus an additional $0.65 per mile. If Eli has at most $10 to spend on the cab ride, how far could he travel?
17 miles
12 miles
23 miles
9 miles
2. Which inequality matches the statement below?
Three-fourths times x added to two times x is more than eleven
3/4x + 2 > 11
2x + 3/4x > 11
3/4(x+2) > 11
3/4 + x + 2 + x > 11
Eli could travel 12 miles and 3/4x+2x>11 inequality matches the statement Three-fourths times x added to two times x is more than eleven
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that a taxi charges a flat rate of $1.75 and an additional $0.65 per mile.
Eli has at most $10 to spend on the cab ride
We need to find how far could he travel
1.75+0.65x≤10
Subtract 1.75 on both sides
0.65x≤10-1.75
0.65x≤8.25
x≤8.25/0.65
x≤12.6
So he could travel 12 miles.
Three-fourths times x added to two times x is more than eleven
3/4x+2x>11
Hence, Eli could travel 12 miles and 3/4x+2x>11 inequality matches the statement Three-fourths times x added to two times x is more than eleven
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Luc is investigating dilations of scale factor 2 of the line y = -4x +3. He claims that for some centers of dilation, the line will remain the same. Which centers of dilation could be used to support Luc's claim? Select ALL that apply.
Luc is correct in stating that the line will remain the same with certain dilation centers, such as the origin (0, 0) and the point (3, -4). These centers of dilation will cause a scale factor of 2, but the line will remain the same.
To check if Luc is correct, we can calculate the points of the dilation with scale factor 2.
For the origin (0, 0):
Point A: (x, y) = (0, 3)
Point B: (x, y) = (-4, -3)
Dilated Point A: (x, y) = (0, 6)
Dilated Point B: (x, y) = (-8, -6)
Equation of the dilated line: y = -4x + 6
This shows that the line is dilated with scale factor 2, but is the same line.
For the point (3, -4):
Point A: (x, y) = (3, -1)
Point B: (x, y) = (-1, -7)
Dilated Point A: (x, y) = (6, -2)
Dilated Point B: (x, y) = (-2, -14)
Equation of the dilated line: y = -4x + 3
This shows that the line is dilated with scale factor 2, but is the same line.
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7
choose the correct answer *
(2 Points)
When Khadija stands at a distance of 18 m from the base of a tree, she forms
an angle of 57° with the top of the tree. What is the height of the tree to the
nearest tenth?
A 27.7 m
B 28.5 m
C 29.2 m
D 301 m
Bree described a yardstick as a length of wood that starts at 0 and continues onto 36 inches. Which geometric term best describes Bree's description of a yardstick
Answer:
The geometric term best described is a line.
Step-by-step explanation:
Given - Bree described a yardstick as a length of wood that starts at 0 and continues onto 36 inches.
To find - Which geometric term best describes Bree's description of a yardstick
Solution -
The geometric term best described is a line.
help me out plz thankyou
Answer: The Last Option. It is very simple.
Answer: D
Explanation:
Overdraft is when you take out more money in your account than your account has.