Using the t-distribution, the 98% confidence interval for the mean temperature is of:
(47.335, 65.624).
What is a t-distribution confidence interval?The confidence interval is given as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the parameters are:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.Using a calculator, the parameters from this sample are given as follows:
[tex]\mu = 56.43, s = 10.198, n = 10[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 10 - 1 = 9 df, is t = 2.82.
The lower bound of the interval is:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 56.43 - 2.82\frac{10.198}{\sqrt{10}} = 47.335[/tex]
The upper bound of the interval is:
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 56.43 + 2.82\frac{10.198}{\sqrt{10}} = 65.524[/tex]
Hence the interval is:
(47.335, 65.624).
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Suppose you had D dollars in your bank account. you spent $12 but have at least $51 left. how much money did you have initially? write and solve an inquality that represents this situation
Answer: D = 39, D = -12 + 51
Step-by-step explanation:
1) Write an equation based off the prompt
D = -12(Spent cash) + 51(Remaining cash)
2) Solve D
D = 39
In a quadrilateral, one angle measures 175.A second angle measures 29, while a third angle measures 54. What is the measure of the remaining angle?
Given:
In a quadrilatral three angle are
[tex]Suppose\text{ }\angle A=175\text{ }\angle B\text{ =29 }\angle C=54[/tex]Required:
Remaining angle i.e.
[tex]\angle D[/tex]Explanation:
In a quadrilatral ABCD
[tex]\begin{gathered} \angle A+\angle B+\angle C+\angle D=360 \\ 175+29+54+\angle D=360 \\ \angle D=360-258 \\ \angle D=102 \end{gathered}[/tex]Final Answer
Remaining Angle= 102
Answer:
102
Step-by-step explanation:
If you add all of the angles (175+29+54) it gives you 258. As you may already know, a quadrilateral's angles have to all equal 360 combined. When you subtract 360-258, you get 102. Hope this helped! :)
What is
−
y
+
9
z
−
16
y
−
25
z
+
4
written in simplest form?
Answer:-15y+-16z+4
Step-by-step explanation:
-y-16y+9z-25z+4
-15y+-16z+4
The speed limit on a road is 30 miles per hour. Drivers on this road typically vary their speed around the
limit by as much as 3 miles per hour. What is the range of typical speeds on this road?
The range of typical speeds (in miles per hour) is
Answer:
Between 30 and 33 mph or, simply
Range: [30,33]
Step-by-step explanation:
A Range is all possible values of a certain variable or piece of information commonly notated by a minimum and maximum. In this example, our variable is the speed traveled by drivers in a road. We are provided a minimum of 30 mph as this is the speed limit, and told that drivers may speed up to a maximum of 3 mph faster ( or 33 mph).
Therefore, our minimum would be 30, maximum would be 33, and Range would be [30, 33].
Brackets are used here because both our minimum and maximum values are included in the range.
HOPE THIS HELPS!!
Need help for my son I will give branliest
The value of a = -10, b = -0.2, c = 0.25
What is an equation?
An equation is a formula that is used to express the equality of two expressions with the help of = sign. In other words, it is an mathematic statement that made two expressions equal. There are different type of equation and we are here dealing with linear equation.
Given equation are,
a) 1/5a = -2
cross multiplying.
a = -2(5)
a = -10
b) 8+b = 7.8
Subtracting,
b = 7.8 - 8
b = 0.2
c) -0,5 = -2c
Dividing,
c = -0.5/-2
c = 0.25
Hence the solution of each equation, is solved above.
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Classify the pair of numbered angles
Answer:
corresponding!!!!!!
Step-by-step explanation:
Corresponding angle is an angle that are one the same side of the transversal lines :))
Hope this helps!!!
Bài 1.5 Tính hạng của các ma trận:
1.
1 2 1 −1 0
2 −1 1 3 4
2 −1 2 1 −2
2 −3 1 2 −2
−4 1 −3 1 8
,
2.
25 31 17 43
75 94 53 132
75 94 54 134
25 32 20 48
Answer:
1 is the awnsewer
Step-by-step explanation:
1
what is the value of h ? give answer in 1 decimal.
trigonometry.
The value of h is 13.3 cm
Let the triangle be ABC where
AB = 18 cm
AC = h cm
∠ABC = 48°
Since, ∠ACB = 90°, therefore the given triangle is a right angle triangle.
We know that
Sinθ = Perpendicular / Hypotenuse
Put θ = 48, we get
Sin 48 = [tex]\frac{h}{18}[/tex]
The value of Sin 48 is 0.74
0.74 × 18 = h
h = 13.3 cm
Therefore the value of h is 13.3 cm
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
600
Step-by-step explanation:
[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]
Help me,what of the following statements is true?Select THREE statements
Three statements are correct and ∠FDE and ∠EDC are supplementary angles .
What is an example of a supplementary angle?
Angles with a supplementary sum are those whose sum is 180 degrees. Angles 130° and 50°, for instance, are supplementary angles as the sum of their respective angles is 180°.When two angles add up to 180 degrees, they are referred to as supplementary angles because they combine to make a linear angle. The opposite is true if the total of two angles is 90 degrees; in this case, they are considered to be complementary angles and together they create a right angle.A) True, ∠BDF and ∠FDE are making linear pair .
C) True, ∠FDE and ∠EDC are supplementary angles .
D) True, ∠ABG and ∠GBD are complementary angles.
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_% of $20 = $10
PLEASE HELP ME ITS IMPORTANT
Answer:
DONT WORRY ITS FIFTY PERCENT
Find the equation of the horizontal line that contains the point (8,4). Express the equation using either the general form or the slope-intercept form of the equation of a line.
The equation of line containing vertices (8,4) is y = 4.
How do you express a line's equation in slope-intercept form?Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). Using y=mx+b to graph a line is typically simple. The standard form and the point-slope form are other formats for linear equations.
Equation of line in slope - intercept form is
y = mx + c
where m= slope
c = y - intercept
As it is given that equation of line is horizontal,
this implies
x = 0
y = m (0) + c
y = c
Now, the given coordinates are (8,4)
Slope of the equation equals 0 As the line is horizontal.
⇒ y = 0 (8) + 4
⇒ y = 4
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Identify the option that shows an example of a dilation with scale factor of 2 given preimage A and image B.
Object dilation for image 1 is 30 cm, image 2 is 21 cm, image 3 is 8 cm, and image 4 is 2 cm.
Dilation is a conversion, which is utilized to resize the thing. Dilation is operated to create things bigger or shorter.
For image 1, Dilation for the given side of polygon A is 10 × 3 = 30cm for polygon B.
Therefore, the dilation for the unknown side of polygon B would be 15 × 3 = 45cm.
For image 2, The dilation for the given side of triangle A is 7 × 3 = 21cm for triangle B.
Therefore, the dilation for the unknown side of triangle B would be 18 ÷ 3 = 6cm for triangle A.
For image 3, Dilation for the given side of triangle A is 12 × 4 = 48cm.
Therefore, the dilation for the unknown sides would be 32 ÷ 4 = 8cm for the left side of triangle A and 8 × 4 = 24 for the right side of triangle B.
For image 4, The dilation for the given side of square A is 2 × 2 = 4cm in square B.
Therefore, the dilation for the unknown side of square A would be 4 ÷ 2 = 2cm for square A.
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Help with statements
Explanation
We are given the following:
We are required to determine the converse, inverse, and contrapositive statements of a conditional statement and also determine whether the statement is true or false.
This is achieved thus:
We know that if P and Q are two simple statements, then
Implication (Conditional): P → Q
Converse: Q → P
Inverse: ~ P → ~ Q
Contrapositive: ~ Q → ~ P
We also know that an implication is false if the antecedent is true and the consequent is false.
Therefore, we have:
ive n statement: I
Let P: A toy block is a clover
Let Q: A toy block is red.
The given statement is true. This is because both statements are true.
Converse: If a toy block is red, then the toy block is a clover.
This statement is false. This is because it is not true for all cases.
Inverse: If a toy block is not a clover, then the toy block is not red.
This statement is true.
Contrapositive: If a toy block is not red, then the toy block is not a clover.
This statement is true.
Hence, the answers are:
I need help with this
We can see that point S is at (2,4), therefore we have to move the point five units down in order to place the point S at (2,-1). The answer would be option C. 5 units.
what is the large cardinal project
The Large Cardinal Project is a field of set theory.
Set theory deals with basic projects. Giant Numbers card attributes are a subset of Infinite Numbers card numbers. The most active set theorists believe that the most important fundamental axioms studied today are compatible with ZFC. Steele and Leber used a giant map to prove the left finite algebraic pyramid theorem (a(bc) = (ab)(ac)). The idea is to introduce the great cardinals to thinkers from the very beginning. It was a little bit good. By definition, a great cardinal is a hypothesis. This aims to show how to establish some basic facts about big numbers by generalizing the combinatorial features of natural numbers to sets of seconds. It is an investigation of important fundamental positions and the axioms of set theory. Numeric Tables and Sequences Overview Aggregates, classes, and numeric tags are not allowed. Some properties of natural numbers Uncountable generalizations.
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Which side of EFGH corresponds with CD
nswer
The side of EFGH that corresponds with CD is GH.
xplanation
One of the key points for two figures to be similar is that the angles are the same.
Since parallelograms have opposite angles equal, and adjacent angles sum up to give 180 degrees. We know that ABC
Angle = 180 - 523 = 127
And this makes the similarity makes the order of similarity here to be
BCD = EFGH
o,
dD = GH
Hope this Helps!!!
Write an expression: 3 times the sum of a number and 5
Answer:
45
Step-by-step explanation:
Evalúe the limit. Show steps
The given limit has its value as 2/3.
The most important calculus rule is known as the L' Hospital's Rule (L'Hôpital's rule). With the help of derivatives, this rule assesses limits involving indeterminate forms. The L'Hospital rule is a general method for evaluating indeterminate forms like∞ / ∞ or /. Calculus derivatives' limits for indeterminate forms are determined using L'Hospital's rule. The L Hospital rule can be applied numerous times.
This guideline recommends differentiating the numerator and denominator by an equal number of times until the confusing or problematic phrase is eliminated for easy understanding.
Since the limit is of the 0/0 type when both the numerator and denominator have h=0, the L Hospital rule can be applied in this situation.
Once the numerator has been differentiated, we obtain Numerator = 2((1/3) + h)
Once the denominator has been differentiated, we obtain Denominator = 1.
As a result of the denominator's complicated factor being eliminated, the limit can now be set.
As a result, the limit at h = 0 has a value of = 2((1/3) + 0)]/1 = 2/3.
As a result, when h=0, the value of the stated limit is 2/3.
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Find the missing angel.Round to the nearest tenth previous answer previous answer 30.2
From the diagram
[tex]\begin{gathered} \theta\text{ = 32} \\ \text{Opp = X} \\ \text{Adj = }5m \\ By\text{ using Pythagoras Theorem we have.} \\ \text{Tan}\theta\text{ = }\frac{Opp}{\text{Adj}} \\ \text{Tan 32 =}\frac{X}{5} \\ X\text{ = Tan 32 }\times5 \\ X\text{ = }3.124m \end{gathered}[/tex]Final answer = 3.124m
please answer ASAP for 100 points and brainliest if possible and if its correct
PLEASE!!!!!!!!!!!!!!!!
Solve each of the following equations using the Extended Square Root Property.
1. 8√x+7=16
x= _____________
2. √7x+4−3=0
x= _____________
3. 8√5x−7=16
x= _____________
Answer:
1) 81/ 64
2)DNE(undefined), and
3)529/64
Step-by-step explanation:
1) 8√x + 7 = 16
8√x = 16 - 7 = 9
√x = 9/8
x = (9/8 )² = 81/ 64
2) √7x+4−3=0
√7x + 1 = 0
√7x = -1
as the square root is always positive, it is impossible.
3) 8√5x−7=16
8√5x = 16 + 7 = 23
√5x = 23/8
5x = (23/8)² = 529/64
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How do i solve this.
A) none of these
B) only mean because if we replace 32 by 16 sum will decrease and so mean will decrease
C) both mean and median because when we remove some value os starting total sum will decrease and hence mean decrease
median will change because after remove some values total number will decrease and hence value will change
d)Negative skewed
What is central of tendency ?Measures of central tendency are the values that characterize a data set by indicating the data's central location. Mean, Median, and Mode are the three primary metrics for determining central tendency.Mean is the product of the sum of all observations and the total number of observations.
An ordered set's median is its middle or centre value.
The most frequent value in a data set is called the mode.
Given that :32, 38, 42, 42, 43, 44, 46, 46, 47, 47, 49, 49, 51, 51, 51, 51, 52, 53, 53, 53, 53, 53
32, 38, 42, 42, 43, 44, 46, 46, 47, 47, 49, 49, 51, 51, 51, 51, 52, 53, 53, 53, 53, 53
mean = [tex]\frac{sum of observation}{number of observation}[/tex]
mean = [tex]\frac{1046}{22}[/tex]
= 47.54
How to calculate median ?The median is calculated by sorting the scores into numerical order, dividing the total by two, rounding the result up to get the median position, or using an even number of scores, averaging the median position's value with the following position's value.
here n = 22 which is even
median =[tex]\frac{\frac{n}{2}term +(\frac{n}{2}+1 )term }{2}[/tex]
[tex]\frac{\frac{22}{2}term +(\frac{22}{2}+1 )term }{2}\\ = \frac{11 term + 12 term}{2}[/tex]
= 49
How to calculate mode ?Organize the numbers in a set in whatever order—from lowest to highest or highest to lowest—and then tally the frequency with which each number appears in the group. The mode is the one that shows up most frequently.
mode = 53 as it is repeated more times.
A) none of these
B) only mean because if we replace 32 by 16 sum will decrease and so mean will decrease
C) both mean and median because when we remove some value os starting total sum will decrease and hence mean decrease
median will change because after remove some values total number will decrease and hence value will change
d)Negative skewed
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2 digit by 2 digit multiplacation 97x57
Answer:
11,280
Step-by-step explanation:
so first you write the equation 97*57. then you multiply them, ( 7*7=49; 5*7= 35, now 9*7= 63; 5*9= 45) and the answer is 11,280
I might be wrong in my calculations because the calculator says the answer is 5,529 so yeah the answer is either 11,280 or 5,529.
Hope this helps
Directions: Watch the directions video for how to complete sample work. You must
answer all questions completely, and show all of your work in order to receive credit.
1. ERROR ANALYSIS
Your friend is trying to find the maximum value of P = -x + 6y subject to the
following four constraints.
(y ≤-2x + 4
y≤ x+1
x≥0
y20
The maximum value of P = 11.
Given: P = -x + 6y
In this question we have to first solve the given system of equations.
Ignore the greater or lesser than sign that is:
y = -2x+ 4 -------- 1
And y = x + 1 --------- 2
On solving these two equations we get;
0= -3x + 3
⇒ -3x = -3
⇒ x= 1
Substituting the value of x in equation 2 we get
y = x+ 1
= 1 + 1 = 2
Thus y = 2 and x = 1
So on putting these values in P = -x + 6y we get
P = - 1 + 6× 2
P = - 1 + 12 = 11
Therefore P= 11.
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8. Harold rode the high-speed train for four
hours and traveled 480 miles. How long
would it take him to travel 960 miles?
A. 2 hours
B. 4 hours
C. 6 hours
D. 8 hours
Please help solve equation
EXPLANATION
The first equation is a line with the following slope-intercept form:
[tex]4x+4y=-8[/tex]Subtracting -4x to both sides:
[tex]4y=-4x-8[/tex]Dividing both sides by 4:
[tex]y=-\frac{4}{4}x-\frac{8}{4}[/tex]Simplifying:
[tex]y=-x-2[/tex]The slope is -1 and the y-intercept is -2
Applying the same reasoning to the second equation we get:
[tex]y=-x+3[/tex]3
Now, we can write and graph both linear equation
your class mate was asked to square (2x - 3) , he answered 4x² - 9 . is his answer correct?
His answer is incorrect
The correct answer is:
[tex]4x^2-12x+9[/tex]This is the square of (2x - 3)
Explanation:Given (2x - 3)
The square of this is:
[tex]\begin{gathered} (2x-3)^2 \\ =4x^2-12x+9 \end{gathered}[/tex]His answer of 4x² - 9 is incorrect.
a figure is made of 2 rectangular prisms...
what is the volume?
The volume of the figure that is composed of two rectangular prisms is: 146 cubic in.
What is the Volume of a Rectangular Prism?The volume of a rectangular prism = (length)(width)(height).
The figure can be decomposed into two rectangular prisms. Find the volume of each of the prisms.
Volume of rectangular prism 1:
Length of the prism = 8 in.
Width of the prism = 7 in.
Height of the prism = 1 in.
Volume of rectangular prism 1 = (8)(7)(1) = 56 in.³
Volume of rectangular prism 2:
Length of the prism = 10 in.
Width of the prism = 9 in.
Height of the prism = 1 in.
Volume of rectangular prism 1 = (10)(9)(1) = 90 in.³
Volume of the figure = 90 + 56 = 146 cubic in.
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Please help with question!!
Given:
[tex]\ln x+\ln (x+14)=3[/tex]Use the formula:
[tex]\ln ab=\ln a+\ln b[/tex][tex]\begin{gathered} \ln x+\ln (x+14)=3 \\ \ln x(x+14)=3 \\ x(x+14)=e^3 \\ x^2+14x=20.085 \end{gathered}[/tex]solve the equation :
[tex]\begin{gathered} x^2+14x=20.085 \\ x^2+14x-20.085=0 \\ x=\frac{-14\pm\sqrt[]{14^2-4(1)(-20.085)}}{2} \\ x=\frac{-14\pm\sqrt[]{276.34}}{2} \\ x=\frac{-14\pm16.623}{2} \\ x=-7\pm8.312 \\ x=-7+8.312;x=-7-8.312 \\ x=1.312;x=-15.312 \end{gathered}[/tex]Answer:
[tex]\textsf{Exact form}: \quad x=-7 +\sqrt{49+e^3}[/tex]
[tex]\textsf{Decimal form}: \quad x=1.312\; \sf (3\:d.p.)[/tex]
Step-by-step explanation:
Given equation:
[tex]\ln x + \ln (x+14)=3[/tex]
[tex]\textsf{Apply the product law} \quad \ln x + \ln y=\ln xy:[/tex]
[tex]\implies \ln (x(x+14))=3[/tex]
[tex]\implies \ln (x^2+14x)=3[/tex]
[tex]\textsf{Apply the log law} \quad e^{\ln x}=x:[/tex]
[tex]\implies e^{\ln (x^2+14x)}=e^3[/tex]
[tex]\implies x^2+14x=e^3[/tex]
Subtract e³ from both sides to form a quadratic equation:
[tex]\implies x^2+14x-e^3=e^3-e^3[/tex]
[tex]\implies x^2+14x-e^3=0[/tex]
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
a = 1b = 14c = -e³Substitute these values into the quadratic formula and solve for x:
[tex]\implies x=\dfrac{-14 \pm \sqrt{14^2-4(1)(-e^3)} }{2(1)}[/tex]
[tex]\implies x=\dfrac{-14 \pm \sqrt{196+4e^3} }{2}[/tex]
[tex]\implies x=\dfrac{-14 \pm \sqrt{4(49+e^3)} }{2}[/tex]
[tex]\implies x=\dfrac{-14 \pm \sqrt{4}\sqrt{49+e^3} }{2}[/tex]
[tex]\implies x=\dfrac{-14 \pm 2\sqrt{49+e^3} }{2}[/tex]
[tex]\implies x=-7 \pm \sqrt{49+e^3}[/tex]
Solutions:
[tex]x=-7 +\sqrt{49+e^3}, \quad x=-7 -\sqrt{49+e^3}[/tex]
Decimal form:
[tex]x= 1.312, \quad x=-15.312[/tex]
As logs of negative numbers cannot be taken, the only solution is:
[tex]x=-7 +\sqrt{49+e^3}\\\\x=1.312\;\sf (3\;d.p.)[/tex]