The distance between the two cars varies at a speed of 65 m/h after two hours.
Let y represent the car's southward travel distance.
Let x be the distance traveled by the westbound automobile.
Allow a to be the distance between the two vehicles.
A right-angled triangle can be used to symbolize these three distances. So, we can state:
a^2 = x^2 + y ^2
Given that the distances vary with respect to time, let's make a distinction.:__________(1)
2a da/dt = 2x dx/dt +2y dy/dt
Rate of distance change between two cars, da/dt
The car is traveling west (dx/dt) at 25 m/h, while the car traveling south (dy/dt) is traveling at 60 m/h.
Therefore:
dy/dt = 60 m/h and dx/dt = 25 m/h
The separation between the two cars will be after two hours:
y = 3* 60 = 180 miles
x = 3 * 25 = 75 miles
Therefore:
a^2 = x^2 + y ^2
a^2 = 75 ^2+ 180 ^2
a= [tex]\sqrt{5625 + 32400}[/tex]
a= 195
From (1):
195(da/dt) = 75(25) + 180(60)
195(da/dt) = 1875 + 10800 = 12675
da/dt = 12675 / 195 = 65 m/h
As a result, after two hours, the two automobiles' separation is varying at a speed of 65 m/h.
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a data analyst creates a scatterplot. the analyst wants to put a text label on the plot to call out specific data points. what function does the analyst use?
The analyst should use the alpha aesthetic. The alpha aesthetic makes some points on a plot more transparent than others to call out specific data points.
What is scatterplot?A set of points plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of correlation, if any, between the values of observed quantities or phenomena, scatter plots are crucial in statistics (called variables). In an effort to demonstrate the degree to which one variable is influenced by another, scatter plots are used to plot data points on a horizontal and vertical axis. The values of the columns set on the X and Y axes determine the position of the marker that represents each row in the data table.
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Can someone help me with this aleks question
For the given triangles ΔTRS and ΔQRP , the required step to prove both the triangles are congruent is ∠TRS ≅ ∠QRP.
As given in the question,
Two triangles ΔTRS and ΔQRP,
It is given that :
Line segment SR ≅ Line segment PR
Line segment SP bisects Line segment TQ
⇒ line segment TR ≅ line segment RQ
∠TRS ≅ ∠PRQ ( by vertically opposite angle )
By Side angle side theorem we have ,
ΔTRS ≅ ΔPRQ
Therefore, for the given triangles ΔTRS and ΔQRP ,the required step to prove both the triangles are congruent is ∠TRS ≅ ∠QRP.
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what is the sum of the exponents of the prime factors of the square root of the largestperfect square that divides 12! ?
8 is the sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!
We are asked the sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!.
As, the largest perfect square that divides 12! is
2^10 * 3^4 *5^2 = 2073600.
Now, the square root of the number 2073600 is,
1440
Now, we have to find the prime factorization of 1440
1440 = 2×2×2×2×2×3×3×5
Now, in the prime factorization of 1440
the exponent of 2 is 5, exponent of 3 is 2 and the exponent of 5 is 1.
So, the sum of the exponents of the prime factors be 5+2+1 = 8
Hence, 8 is the sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!
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Justify each of the following manipulations to multiply two binomials by filling in the blanks with the associative property the commutative property or the distribution (3x+5)(2x+7)=2x(3x+5)+7(3x+5) helpppp!!
The property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.
In this question we have been given an expression.
We need to identify the property that is used to multiply two binomials.
(3x+5)(2x+7)=2x(3x+5)+7(3x+5)
Consider two binomials,
(3x+5)(2x+7)
= (2x+7)(3x+5) ...............(commutative property)
= 2x(3x+5)+7(3x+5) ................(distributive property)
Therefore, the property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.
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HELP ME PLEASEEEEEEE
Answer:
[tex]{ \boxed{ \tt{ \sin( \theta) = \frac{opposite}{hypotenuse} }}}[/tex]
- \theta = 25°
- opposite = x
- hypotenuse = z
[tex]{ \tt{ \sin(25 \degree) = \frac{x}{z} }} \\ [/tex]
Answer: x/z
Step-by-step explanation:
sin25 uses soh from sohcahtoa
sin25 = opposite/hypotenuse = x/z
Please help
The equation y = -8/3x + 40 represents an alternative speed slide the city of Geocove is thinking of constructing in their waterpark. The graph of this equation is shown. Suppose that a rider travels downward 8 feet on this slide. What is the value of their horizontal change?
6 feet
2.7 feet
8 feet
3 feet
The value of their horizontal change is 2.7 feet
How to determine the value of their horizontal change?The equation of the function is given as
y = -8/3x + 40
From the question, the distance travelled by the rider is given as
Distance = 8 feet downward
This means that
Horizontal change = slope
A linear equation is represented as
y = mx + c
Where
Slope = m
By comparing y = mx + c and y = -8/3x + 40, we have
Slope = m = 8/3
This gives
Horizontal change = 8/3
Evaluate
Horizontal change = 2.7
Hence, the horizontal change is 2.7 feet
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2x-84=108
x=?
please help
Answer:
X=
Step-by-step explanation:
Let's solve your equation step-by-step.
2x−84=108x
Step 1: Subtract 108x from both sides.
2x−84−108x=108x−108x
−106x−84=0
Step 2: Add 84 to both sides.
−106x−84+84=0+84
−106x=84
Step 3: Divide both sides by -106.
−106x
−106
=
84/−106x=−42/53
PLEASE HELP 69 POINTS
Triangle A has vertices (−2, 1), (1, 1), and (1, 0).
Which triangle is similar to triangle A?
Responses
Triangle Y with vertices (−4, 3), (2, 3), and (2, 2)
Triangle W with vertices (−4, 2), (2, 2), and (2, 0)
Triangle X with vertices (−2, 2), (1, 2), and (1, 0)
Triangle Z with vertices (−4, −1), (2, −1), and (2, −2)
The triangle with vertices (−2, 1), (1, 1), and (1, 0) is similar to
Triangle W with vertices (−4, 2), (2, 2), and (2, 0)What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions.
Examining the vertices shows that; Triangle W with vertices (−4, 2), (2, 2), and (2, 0) is in proportion to the given vertices (−2, 1), (1, 1), and (1, 0)
The difference is a scale factor of 2
(−2, 1) * 2 = (−4, 2)
(1, 1) * 2 = (2, 2)
(1, 0) * 2 = (2, 0)
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Which of these strategies would eliminate a variable in the system of equations?
2x + 8y = -3
3x + 6y = -4
A: Multiply the top equation by 333, multiply the bottom equation by -2−2minus, 2, then add the equations.
B: Multiply the top equation by 333, multiply the bottom equation by 444, then subtract the bottom equation from the top equation.
C: Multiply the top equation by -4−4minus, 4, multiply the bottom equation by 333, then add the equations
Option A: Multiply the top equation by 3, multiply the bottom equation by -2, then add the equations will eliminate the variables.
Rewriting the equation -
2x + 8y = -3 : Equation 1
3x + 6y = -4 : Equation 2
Multiplying equation 1 with and equation 2 with -2.
6x + 24y = -9 : Equation 3
-6x - 12y = 24 : Equation 4
Adding the equation 3 and equation 4. This will eliminate the variable x.
12y = 15
y = 5/4
So, option 1 will eliminate the variable x on solving we get the value of y as 5/4.
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The perimeter of this triangle is not more than 30 cm. 2n+3 cm, 2n+2 cm, n cm
a. Write an inequality to show this.
b. Solve the inequality.
c. What are the largest possible lengths of the sides?
The inequality to represent the perimeter of the triangle is given by (2n + 3) + (2n + 2) + n ≤ 30
The solution to the inequality is n ≤ 5 The largest possible lengths of the sides is 13 cmInequality to represent the perimeter of a trianglePerimeter of the triangle = not more than 30 cmSide a = (2n + 3)cmSide b = (2n + 2) cmSide c = n cmSide a + side b + side c ≤ perimeter of the triangle
(2n + 3) + (2n + 2) + n ≤ 30
open parenthesis2n + 3 + 2n + 2 + n ≤ 30
5n + 5 ≤ 30
substract 5 from both sides
5n ≤ 30 - 5
5n ≤ 25
divide both sides by 5n ≤ 25/5
n ≤ 5 cm
The largest possible lengths of the sides is:
Side a = (2n + 3)cm
= 2(5) + 3
= 10 + 3
= 13 cm
Side b = (2n + 2) cm
= 2(5) + 2
= 10 + 2
= 12 cm
Side c = n cm
= 5 cm
So therefore, the largest possible length of the triangle is 13 cm
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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
32 kg to 56 kg
Answer:
4/7
Step-by-step explanation:
32:56
32÷2=16
56÷2=28
16:28
16÷2=8
28÷2=14
8:14
8÷2=4
14÷2=7
4:7
32:56 ~ 32/56
=4/7
Como puedo Terminar la sucesion asta el decimo termino 3.8 +2.7
The addition of the decimals given as 3.8 and 2.7 will be 6.5.
What are decimals?Decimals simply means the numbers that are not whole numbers. They consist of whole numbers and fractions. Examples include 3.6, 2.1 eyc.
In this case, we want to find the value of 3.8 and the addition to 2.7. This will be:
= 3.8 + 2.7
= 6.5
Therefore, the value is 6.5.
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A sample of size 50 from a normal distribution has sample mean 5 and sample variance 20. Find 96% confidence intervals for the variance and standard deviation of the distribution.
The standard deviation and variance of the distribution's 96% confidence intervals are 9.841 and 5.704, respectively.
A normal distribution sample of size 50 has an expected higher rate of 20 and a sample mean of 5.
n = 50 makes up the sample size.
Furthermore, the sample variance is s² = 20
The following is the formula for both the variance confidence interval:
σ² = [tex](\frac{(n-1)s^2}{X^2_{{n-1};{1-\alpha /2}}}, \frac{(n-1)s^2}{X^2_{{n-1};{\alpha/2}}})[/tex]
Here, [tex]{X^2_{{n-1};{1-\alpha /2}}}[/tex] is the critical value at the status of significance [tex]\alpha[/tex] & degree of freedom n - 1.
The 90% confidence interval's lower bound for variance is stated as,
[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (30.114)
= 32.54
The 90% confidence interval's upper bound for variance is stated as,
[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (10.117)
= 96.86
Consequently, the confidence level for the distribution's variance is (96.86, 32.54).
Additionally, the range of the distribution's standard deviation inside the 90% confidence interval is (√96.86, √32.54), that's the same as (9.841, 5.704).
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help meeeeeeeeeee pleaseeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The dive lasted approximately [tex] \boxed{\sf 2.76} [/tex] seconds.
Step-by-step explanation:
Given formula: h = 16t²
Where, t is time in seconds and h is the distance in feet traveled by a free-falling body or object.
According to the question,
Height of the cliff from which diver dives (h) = 122 feet.
By substituting the value of height in the formula we get:
[tex]\rm \implies 122 = 16 {t}^{2} \\ \\ \rm \implies {t}^{2} = \dfrac{122}{16} \\ \\\rm \implies {t}^{2} = 7.625 \\ \\ \rm \implies t = \sqrt{7.625} \\ \\ \rm \implies t = 2.76 \: seconds[/tex]
Decrease 330 km by 54%.
Answer: 151.8
Step-by-step explanation:
330/100 x 54 = 178.2
330- 178.2 = 151.8
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations that can be used to solve for y, the length of the room
y2 – 5y = 750 750 – y(y – 5) = 0 (y + 25)(y – 30) = 0How do we obtain the relevant equations that can be used for the problem?First and foremost, we can begin solving this equation by noting the formula for calculating the area of a rectangle. This formula is given as follows:
Area of a rectangle = Length × Width
Since the width of the room is 5 feet less than the length of the room, we will have the resulting equation as the area of the rectangle:
y( y - 5) = 750
When this equation is fully expressed, we will get the following equations:
y2 – 5y = 750 750 – y(y – 5) = 0 (y + 25)(y – 30) = 0Therefore, options, B, C, and E are correct.
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Given: AD
Prove: DE
A
D
BC and ZBCD ZADC
CE
C
Intro
B
Correct! Assemble the next
statement.
Angles Segments Triangles Statements Reasons
SAS
CPCTC
reflexive property
Statements
✓1. AD BC
✓ 2. ZDEA and CEB are
vertical angles
3. ZBCD
ZADC
vertical angles theorem
Reasons
1. given
2. def. of vertical angles
3. given
Triangle ADC and ΔBDC are congruent. then DE ≅ CE
What do you mean by congruent?
It is claimed that two figures are "congruent" if they can be positioned exactly over one another. Both the shape and size of the bread slices are same if you lay one slice on top of the other. Congruent refers to having precisely the same form and size.Given,
AD ≅ BC
∠BCD ≅ ∠ADC
In triangle ADC and ΔBDC
AD ≅ BC ( GIVEN )
∠BCD ≅ ∠ADC ( GIVEN )
DC = DC ( Common line)
so triangle ADC and ΔBDC are congruent.
then DE ≅ CE
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Solve for X please help
Answer:
17
Step-by-step explanation:
4x-10=58(alternate interior angles)
4x=68
x=17
You have 7,160 grams of a radioactive kind of bismuth. How much will be left after 10 days if
its half-life is 5 days?
grams
The solution is 1790 grams
The amount of bismuth left after 10 days if the half life is 5 days will be
1790 grams
What is half-life of an element?
The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.
Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value
The decay constant λ is = 0.693/t½
where t½ is the half-life of the element
Given data ,
Let the half life of the element be represented as t½
The value of t½ = 5 days
Now , the initial amount of bismuth N₀ = 7160 grams
The number of days t = 10 days
The amount of bismuth left after 10 days = N( t )
Now , the value of N( t ) is given by the formula ,
N( t ) = N₀ ( 1/2 )^ t/ t½
Substituting the values in the equation , we get
N( t ) = 7160 ( 1/2 )^10/5
N( t ) = 7160 ( 1/2 )²
N( t ) = 7160 / 4
N( t ) = 1790 grams
Therefore , the value of N( t ) is 1790 grams
Hence , the amount of bismuth left is 1790 grams
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how many cubes are added
The number of centimeter cubes to be added to make the cuboid is; 30 cubes.
How to Interpret the elevation of objects?From the given plan, side elevation and front elevation, we can see that the number of cubes needed to make the shape is 18 blocks.
From the front elevation, 12 blocks is required (4 * 3 blocks).
From the side elevation, 6 blocks are required which gives us a total of 18 blocks.
The number of blocks needed to make the given cuboid is;
Volume of cuboid = 4 * 4 * 3 = 48 cm cubes.
Therefore the number of cubes to be added = Volume cubes - Number of cubes from elevation
The number of cubes to be added = 48 cubes - 18 cubes
The number of cubes to be added = 30 cubes.
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avoiding an accident when driving can depend on reaction time. that time, measured from the moment a driver sees the danger until he/she gets his/her foot on the brake pedal, is normally distributed with a mean of 1.5 seconds and a standard deviation of 0.18 seconds. what is the interquartile range of the reaction times? report your answer to at least the nearest hundredth of a second (i.e. with at least two digits after the decimal point).
The interquartile range of the reaction times is 0.528 or 52.80%
A normal model is represented as (μ, σ). Therefore for (1.5, 0.18), the mean (μ) = 1.5 and the standard deviation (σ) = 0.18
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
The z score shows by how many standard deviations the raw score is above or below the mean. It is given as:
The interquartile range is x = 1.45 and x = 1.75
For x = 1.45
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
Z=(1.45-1.5)/0.18
= -0.28
For x = 1.75
Z=(1.75-1.5)/0.18
= -1.39
From the normal distribution table,
P(1.45 < x < 1.75) = P(-0.28 < z < 1.39)
= P(z < 1.39) - P(z< - 0.28)
= 0.9177 - 0.3897
= 0.528
= 52.8%
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Can anyone write the equation of the graph?
Simplify negative 1 and 2 over 3 minus 9 and 2 over 5.
11 and 1 over 15
negative 10 and 4 over 8
negative 16 over 15
negative 166 over 15
The simplified form of the given expression; negative 1 and 2 over 3 minus 9 and 2 over 5 as required is; -166/15 (negative 166 over 15).
What is the simplified form of the expression?It follows from the task content that the simplified form of the given expression is to be determined.
Since the given expression is; -1 ⅔ - 9 ⅖.
First, the mixed numbers as in the task content must be converted to fractions so that we have;
- 1 ⅔ = -5/3 and
9 ⅖ = 47/5
Therefore, the required evaluation is; -5/3 - 47/5
= -25/15 - 141/15
= (-25 - 141) / 15
= -166/15
Therefore, the required simplified form of the expression is; negative 166 over 15.
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NEED HELP FINDING THE EQUATION!!! THXXXX
Answer:
See below
Step-by-step explanation:
Horizontal lines have ZERO slope
Vertical lines have 'undefined' slope
for this example x = 1/2 includes the point and has undiefined slope
find the median of the following: 14.8, 16.2, 4.8, 12.1, and 6.9. if needed, round your answer to the nearest tenth.
The mean will be the middle number or 12.1.
What is mean?In mathematics and statistics, the concept of mean is crucial. The most typical or average value among a group of numbers is called the mean.It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "expected value."There are different ways of measuring the central tendency of a set of values. There are multiple ways to calculate the mean. Here are the two most popular ones:Arithmetic mean is the total of the sum of all values in a collection of numbers divided by the number of numbers in a collection.According to our question-
The median is the middle number in the data set when the data set is written from least to greatest.
least to greatest 4.8, 6.9, 12.1, 14.8, 16.2
Hence, The mean will be the middle number or 12.1.
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simplify 1/x^-5 HELP ME PLEASE FIRST ANSWER GETS BRAINLIEST
Answer:
x^5
Step-by-step explanation:
Add/Subtract Rational Numbers :
Add ; -1/2 + 2/3 (Simplify)
Evaluate ; -1/8 - (-5/6) (Simplify)
In a two-digit number, the unit digit is 5 more than the tens digit. The number itself is three times the sum of the digits. What is the number?
Answer:
27
Step-by-step explanation:
You want a 2-digit number that is 3 times the sum of its digits, where the units digit is 5 more than the tens digit.
SetupLet t represent the tens digit. Then the units digit is (t+5) and the sum of digits is ...
t +(t +5) = 2t+5
The value of the number is ...
10t +(t+5) = 11t +5
The value is 3 times the sum of digits, so we have ...
11t +5 = 3(2t +5)
Solution11t +5 = 6t +15
5t = 10 . . . . . . . . . . subtract (6t+5)
t = 2
(t+5) = 7
The number is 27.
Solve for a side in right triangles
Really need help with this one!!
The value of side AC is AC = 3.
What is right triangle?
A right triangle, also known as a right-angled triangle, an orthogonal triangle, or historically a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angles.
The given triangle ΔABC is a right angled triangle.
So, to find the side AC we can use the cosine ratio,
[tex]cosB = \frac{Adjacent side}{Hypotenuse}\\ cos65 = \frac{AC}{AB} \\cos65 = \frac{AC}{7} \\AC = 7(c0s(65)\\AC = 7(0.4226)\\AC = 2.9583[/tex]
AC ≈ 3.
Hence, the length of side AC is 3.
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7. The total cost of Mrs. Goodwin's donut purchase varies directly with the amount of donuts purchased. If
the total cost was $7.50 for 15 donuts, how many donuts can she purchase for $10.00?
The number of donuts that can be purchased for $10 is 20.
The total cost of Mrs. Goodwin's donut purchase varies directly with the number of donuts purchased. The total cost of 15 donuts was $7.5. We need to find out the number of donuts that can be purchased for $10.
Let the number of donuts, price, and constant of proportionality be represented by the variables "n", "p", and "k", respectively.
The price is directly proportional to the number of donuts purchased.
p ∝ n
We will remove the proportionality sign.
p = k*n
7.5 = k*15
k = 1/2
The equation is p = (1/2)n. We will now calculate the number of donuts that can be purchased for $10.
p = (1/2)n
10 = (1/2)n
n = 10*2
n = 20
Hence, the number of donuts that can be purchased for $10 is 20.
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