You can use the hypotenuse formula, e.g., from the Pythagorean theorem calculator, to estimate the diagonal of a rectangle, which can be expressed with the following formula: d² = l² + w², and now you should know how to find the diagonal of a rectangle explicit formula - just take a square root: d = √ (l² + w²).
Which expression is equivalent to
94
94
310
95
94
310
(9².3³) ²₂
Answer:
Step-by-step explanation: The simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.
What is an integer exponent?
In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
The question is incomplete.
The complete question is attached in the picture, please refer picture.
We have an expression:
Thus, the simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.
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Expandthis please (x+2y) 5
Answer:
5x+10y
Step-by-step explanation:
to expand we distribute each term with 5
5(x)+5(2y)
5x+10y
Hopes this helps please mark brainliest
Answer: 5x + 10y
Step-by-step explanation:
Re-order terms so constants are on the left
(x+2y)x5
5(x+2y)
Distribute
5(x+2y)
5x+10y
if someone could help me out on this that would be great! (will mark brainliest if optional)
Answer:
(3, 6)
Step-by-step explanation:
I hope this helps you!
10 POINTS!
What is the equation of the line in standard form?
(-3,2) and (2,-1)
Answer: y = -.06x + 0.2
Step-by-step explanation: Find the slope by plugging in the given values to the slope formula to find that the slope is -0.6. Next, determine the y-intercept is b=y1−m⋅x1: b = 2 - (-0.6) ⋅ (-3) = 0.2 Finally, the equation of the line can be written in standard form y= -0.6x + 0.2.
Solve for X please help
Answer:
17
Step-by-step explanation:
4x-10=58(alternate interior angles)
4x=68
x=17
decide whether the following situation is looking for part, the percent, or the whole.
81 of 270 pages in a book
PLEASE HELP quick it would help
81 of 270 pages in a book is a part of the situation.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
81 of 270 pages in a book.
Eighty one of two hundred seventy pages in a book.
In the given situation, A book has 270 pages in that we have taken 81 pages which are part of the book.
We have taken pat of the book,
In the given situation, book is whole and 81 is the part.
Hence 81 of 270 pages in a book is a part of the situation.
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the reaction time of a driver to visual stimulus is normally distributed with a mean of 0.4 seconds and a standard deviation of 0.005 seconds. what is the probability that a reaction requires more than 0.5 seconds?
Answer:0.02275
Normal distribution:
Which is symmetrical about mean.
Mean:
It is the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.
Complement rule:
When two disjoint sets are meant to occur then the sets are said to be complementary.
Given:
Mean= 0.4 seconds
Standard deviation= 0.005 seconds
Let, X be the reaction time for the driver to view stimulus.
So, distribution of X is given by:
X~ N( 0.4, 0.005)
Where σ= 0.05 and µ= 0.4
Solving this ques by using normal standard deviation and z score given as:
z=\frac{x-µ}{σ}
Applying formula:
P(X>0.5)= P{(x-µ/σ) > (0.5-µ/σ)} P {Z > (0.5-0.4/0.05)}
=P(Z > 2)
By using complement rule we get,
P(Z>2) = 1- P(Z<2)
Using normal standard table we have,
P(Z>2)=1- P(Z<2)
= 1- 0.97725
= 0.02275
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The probability that a reaction requires more than 0.5 seconds is 0.0227
Z-score standardization:
The amount of standard deviations the data point deviates from the mean is shown by the standardized z-score.
• If the z-score increases when it is higher than the mean (0).
• If the z-score is below the mean and takes a negative value (0).
Given that,
Mean = μ =0.4
Standard deviation = σ =0.005
The probability that a reaction requires more than 0.5 seconds is obtained by;
Let X denotes the reaction time of a driver which follows a normal distribution with a mean of 0.4 seconds and a standard deviation of 0.005 seconds.
P(X > 0.5) = 1 - P(X < 0.5)
= 1 - P(0.4 < X < 0.5) (0.5 - 0.4/0.005)
= 1 - P(25.06)
= 1 - P(252)
From the “standard normal table”, the area to the left of is 0.9773.
P(X > 0.5) = 1 - P(252)
= 1 - 0.9773
= 0.0227
Hence, the probability that a reaction requires more than 0.5 seconds is 0.0227
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what is the probability that 5 hearts are chosen if 8 cards are chosen from a well-shuffled deck of 52 playing cards?
The probability that 5 hearts are chosen if 8 cards are selected from a well-shuffled deck of 52 playing cards is 0.0156296302.
The number of choosing 8 cards out of 52 is = ⁵²C₈
Number of ways of choosing 5 cards of heart out of 13 cards and 3 out of remaining 39 cards = ¹³C₅ × ³⁹C₃
Probability of choosing 5 hearts = ¹³C₅ × ³⁹C₃ / ⁵²C₈
= 1287 ×9139 / 752538156
= 11761893 / 752538156
= 0.0156296302
A basic 52-card deck consists of 13 ranks in each of the four French suits: clubs, diamonds, hearts, and spades. Each card includes three court cards (face cards), King, Queen, and Jack, as well as reversible (double-headed) images. Each card also contains ten numeral cards or pip cards, from one to ten.
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sarah owns a farm and has lots of dogs on her property. in the table below, she has listed each of her dogs by name and has classified them according to size and color. at random, she picks one of the dogs to take with her to the pet store. what is the probability the selected dog is medium and brown?
The probability the selected dog is medium and brown by Sarah is 6/49.
What is meant by the word probability?A field of mathematics that deals with the exploration of probabilities. The ratio of that number of alternatives in an exhaustive set all equally probable scenarios that cause a specific event to that same total number of conceivable outcomes.Probability = favourable outcome/ total outcome
The table for the given question is attached.
Total dogs owned by Sarah = 7.
Total medium sized dogs = 2.
Total brown coloured dogs = 3
Probability( medium sized ) = 2/7
Probability( brown coloured ) = 3/7
Probability( medium sized and brown coloured ) = (2/7)×(3/7)
Probability( medium sized and brown coloured ) = 6/49
Thus, the probability the selected dog is medium and brown is 6/49.
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(Irrational Numbers MC)
Approximate -17 √√60 to the nearest tenth.
O-9.3
-7.7
7.7
9.3
Question 6(Multiple Choice Worth 2 points)
(Multiplying and Dividing with Scientific Notation MC)
The value of the square root of 60 subtracted from 17 is D. 9.3
How to illustrate the informationIt's important to note that a square root simply means the number that you can multiply by itself in order to get the original number.
In this case, the information given regarding the numbers is illustrate below:
= 17 - ✓60
= 17 - 7.7
= 9.3
Therefore, the value is.9.3
The correct option is D.
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Solve :-
[tex]7a - 3 = 3 + 6a[/tex]
Answer:
A=6Step-by-step explanation:
7a-3=3+6aMove 6a to the other side
7a-6a-3=3Subtract 7a and 6a
a-3=3use inverse operations. So add 3 on both sides
a-3+3=3+3~~~~~~~~~Now we have the answer which is a=6Answer:
a = 6
Step-by-step explanation:
The given equation is,
→ 7a - 3 = 3 + 6a
Now the value of a will be,
→ 7a - 3 = 3 + 6a
→ 7a - 6a = 3 + 3
→ a = 3 + 3
→ [ a = 6 ]
Hence, the value of a is 6.
HELPPPP I NEED THIS QUICKLY!!
A) Yes it is a function and f(x)=2.80+3.50x so 2.80 is an independent function and 3.50x is dependent function
B) Domain x = (0,20] and Range y = (2.8,72.8]
A dependent function is what?
A dependent function type is one whose outcome depends on the parameters of the function.
Independent function: What is it?
Independent function (plural independent functions) as a noun (mathematics) any one of a group of functions whose value cannot be inferred from the values of all the others.
Given: The expression y = 3.5x + 2.8 calculates the y (in dollars) cost of an x-mile taxi fare. You have enough cash to take a cab for a maximum of 20 kilometres.
Domain and range to find
Solution:
y = 3.5x + 2.8
cost y (in dollars)
miles, in.
You have enough cash to take a cab for a maximum of 20 kilometres.
0 < x ≤ 20
Therefore, x = [0, 20].
Domain x = [0, 20]
y = 3.5x + 2.8
x = 0
=> y = 0 + 2.8 = 2.8
x = 20
=> y = 3.5(20) + 2.8
=> y = 70 + 2.8
=> y = 72.8
2.8 < y ≤ 72.8
y = (2.8 , 72.8 ]
Range = (2.8 , 72.8 ]
Learn More :
Find the domain and range of the function f(x)= √9-x² . OR. Let f ...
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Consider this function. f(x) = |x – 4| + 6 If the domain is restricted to
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Ocean sunfish are well-known for rapidly gaining a lot of weight on a diet based on jellyfish. the relationship between the elapsed time, ttt, in days, since an ocean sunfish is born, and its mass, m(t)m(t)m, left parenthesis, t, right parenthesis, in milligrams, is modeled by the following function:
Every day mass of sunfish is multiplied by factor of (ln(67/50)/6).
In the given question we have a relation between mass of sunfish and time elapsed t. Relation is
M(t) = (67/50) ^(t/6+4) -----(1)
To find out the factor which multiple by mass of sunfish each day, we can take derivative of M(t) function.
Derivative of a function measures the change in fucyion value with respect to change in its argument. It gives rate of change of function with respect to change in given variable value. So, in this problem derivative of mass function M(t) gives the rate of change of M(t) with respect to time , t .. It is represented by dM(t)/ dt.
dM(t)/ dt =( 67/50)^(t/6+4) (1/6)ln(67/50)
We have the used derivative formula d(a^t)/dt = a^t (1) lna
dM(t)/dt = ln(67/50)/6 (67/50)^(t/6+4)
dM(t)/dt = (ln(67/50))/6 M(t)
We can see here that mass funtion is increased by factor ln(67/50)/6 each day.
#Complete question:
Ocean sunfish are well known for rapidly gaining a lot of weight on a diet based on jellyfish. The relationship between the elapsed time, t, in days, since an ocean sunfish is born, and it’s mass, M(t), in milligrams, is modeled by the following function:
M(t)=(1.34)^t/6+4
Complete the following sentence about the daily rate of change in the mass of the sunfish. Round your answer to two decimal places.Every day, the mass of the sunfish is multiplied by a factor of _______.
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Rafael has saved up $650 to buy a new laptop. The laptop he wants is in stores for $749.99 but is on sale for 25% off. After the discount is removed, a tax rate of 5.75% is added on. After Rafael buys the laptop, how much money will he have left over? Remember to round to the nearest hundredth as you go because this is money.
The amount of money left over after buying the laptop is $55.17.
How to calculate the value?From the information, the laptop he wants is in stores for $749.99 but is on sale for 25% off and after the discount is removed, a tax rate of 5.75% is added on.
This will be:
= $749.99 - (25% × $749.99)
= $749.99 - $187.50
= $562.49
The addition of the tax will be:
= $562.49 + (5.75% × $562.49)
= $562.49 + $32.34
= $594.83
The money left over will be:
= $650 - $594.83
= $55.17
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Standing on top of a 200 m building with the estimation angle of depression from the top of the building to a park bench on the ground to be 54°
How far is the park bench is from the foot of the building
Distance of Park bench from building is 275 m when angle of depression top of the building to a park bench on the ground.
What is the elevation and depression angle?
The angle between the horizontal and an item is referred to as its elevation. The line of sight of an observer would be upward. Angle of depression refers to the downward angle from the horizontal to an item.Angle of depression, θ = 54°
The height, h = 200
The distance of park bench from the building, d is given by
Tan θ = opposite / Adjacent
Tan 54 = d / 200
d = 200 * Tan 54
d = 200 * 1.3764
d = 275.28
D = 275 M
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Order from least to greatest 3.706, 3.76, 2.5991, 3.7
Answer:
2.5991 < 3.7 < 3.706 < 3.76
Step-by-step explanation:
I believe the they're being multiplied by one, but I have no idea
The values, 1:5, 6:30, 10:50, 11:55 and 18:90, will complete the given ratio table.
According to the question,
We have the following information:
We have a ratio table where two rows from the beginning are given.
In these rows, we have 1:5 and 6:30.
Now, we can easily find that the number in the second column is found by multiplying 5 into the number in the first column.
Now, for the third row, we have the number in the second column,50:
x*5 = 50
x = 50/5
x = 10
Third row: 10 to 50
Fourth row:
Number in the first column = 11
11*5 = 55
11:55
Fifth row:
Number in the first column = 18
18*5 = 90
18:90
Hence, the values, 1:5, 6:30, 10:50, 11:55 and 18:90, will complete the given ratio table.
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Which variable is most important to the following problem?
A company has 95,000 shares of stock to sell. A stockbroker decides to buy equal shares of the stock for each of her 250 clients. If the company has 75,000 shares of stock remaining after she makes her purchase, how many shares did each client receive?
The number of shares remaining after the stockbroker buys shares for her customers is 57500
Also, The number of the most important pretty definitely really variable for finding the number of shares the company particularly definitely for all intents and purposes has left in a generally really big way in a fairly big way. Also, The number of shares the company generally really definitely has left after stockbroker's purchase = 95000 - 150×250 = 5750 in a subtle way.
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Describe a data set that has an outlier. How does the outlier affect the residual? Explain.
A data point that is outrageously high or wildly low in comparison to the closest data point and the majority of the adjacent coexisting values is referred to as an outlier in the dataset or data graph you're working with.
What is a data set?A data set is a group of related data. In the case of tabular data, a data set relates to one or more database tables, where each row refers to a specific record in the corresponding data set and each column to a specific variable.Data set with an outlier:
In a data graph or dataset, you're dealing with, an outlier is a data point that is wildly high or wildly low in comparison to the closest data point and the rest of the nearby coexisting values. Outliers are extreme values that significantly deviate from the dataset's or graph's normal distribution of values.Observed data points that deviate greatly from the least-squares line are known as outliers. They have significant residuals, which are measured as the vertical separation between the line and the point. It is important to carefully investigate outliers. Sometimes, for a variety of reasons, they ought to be excluded from the data analysis.Therefore, a data point that is outrageously high or wildly low in comparison to the closest data point and the majority of the adjacent coexisting values is referred to as an outlier in the dataset or data graph you're working with.
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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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$15,000 is deposited into an account that pays 6.25% annual interest, compounded weekly. Find the balance after 7 years.
Answer: (if A=P(1+rt) is your formula)
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 6.25%/100 = 0.0625 per year.
Solving our equation:
A = 15000(1 + (0.0625 × 7)) = 21562.5
A = $21,562.50
The total amount accrued, principal plus interest, from simple interest on a principal of $15,000.00 at a rate of 6.25% per year for 7 years is $21,562.50.
Which of the following equations shows a directly proportionate relationship?
y = -4x
y = 3x - 1
y = 2.75x - 3
y = 7x
Answer:
first and third
Step-by-step explanation:
the equation representing direct proportion is
y = kx ← k is the constant of proportion
y = - 4x is in this form with k = - 4
y = 7x is in this form with k = 7
Help quick, State if the two triangles are congruent. If they are state how you know.
The two triangles are congruent and they are congruent by ASA.
How to ascertain if triangles are congruent?Triangles are congruent when they have exactly the same three sides and exactly the same three angles. This simply implies the corresponding sides and angles of the triangles are congruent.
Let's check if the triangles are congruent.
One of the congruent angles in the triangles are vertically opposite angle.
Recall vertically opposite angles are congruent.
In these two triangles, we have a congruent angle pair and a congruent side pair.
Therefore, we can say the triangles are congruent by ASA.
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The speed of light is about 3 × 105 kilometers per second. The distance between Earth and the Moon is about 3.84 × 105 kilometers. Find how long it would take for light to travel from Earth to the Moon.
In scientific notation
The time it would take for light to travel from Earth to the moon is; 1.28 seconds.
How long would it take to travel from Earth to the moon?It follows from the task content that the time it would take for light to travel from Earth to the Moon is to be determined.
Since the given speed of light is; 3 × 10⁵ km/s and the distance is; 3.84 × 10⁵ km.
It follows from the formula;
Speed = Distance / Time
Time = Distance/Speed
Time = 3.84 × 10⁵ / 3 × 3.10⁵
Time = 1.28 seconds.
Therefore, the required time it would take to travel from Earth to the moon is; 1.28 seconds.
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how would you respond to a statement that says that by increasing the sample size, the amount of sampling error will be decreased?
The statement about That by increasing the sample size, the amount of sampling error will be decreased is true.
Given that,
That by increasing the sample size, the amount of sampling error will be decreased
Sampling error is inversely related to sample size. Therefore, if we expand the size of our sample, the likelihood of sampling error is reduced and the results are more trustworthy. The standard error is the term used to describe the sampling error that is most frequently utilized (SE). A measurement of the range of estimations around the "actual value" is the standard error. You get a lower return by increasing the sample size beyond what you already have because the added accuracy won't make much of a difference.
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What is cos 60°?
A.1
B. √3/2
C. √3
D.1/2
E.1/√2
F.1/√3
Answer:
The trigonometric functions, sin, cos and tan for an angle are the primary functions. The value for cos 60 degrees and other trigonometry ratios for all the degrees 0°, 30°, 45°, 90°, 180° are generally used in trigonometry equations. These trigonometric values are easy to memorize with the help trigonometry table.
Cos 60 Degree Value
In a right-angled triangle, the cosine of ∠α is a ratio of the length of the adjacent side (base) to the ∠α and its hypotenuse, where ∠α is the angle formed between the adjacent side and the hypotenuse.
Cos 60 Degree value
Cosine α = Adjacent Side / Hypotenuse
Cos α = AC / AB
Cos α = b / h
Now, to find the value of cos 60 degrees, let us consider, an equilateral triangle ABC as given below:
Cos 60 Degree
Here, AB = BC = AC and AD is perpendicular bisecting BC into two equal parts.
As we know, cos B = BD/AB
Let us consider the length of each side as 2 units, such as AB = BC = AC = 2 units and BD = CD = 1 unit.
Therefore, the value of cos 60° = BD/AB = ½
In the same way, we can write the value of sin 60° and tan 60° by evaluating the required sides.
In right triangle ABD, by Pythagoras theorem:
AB2 = AD2+ BD2
22 = AD2 + 12
AD2 = 22 -12
AD2 = 4 – 1
AD2 = 3
AD = √3
Now, we have got all the sides of triangle ABD.
Sin 60° = AD/AB = √3/2
Tan 60° = AD/BD = √3 / 1 = √3
We can also write the value of cos 60 degrees in decimal form as:
cos 60° = 1/2 = 0.5
Also, we can write the values of sine, cosine and tangent with respect to all the degrees in a table.
Let us draw a table with respect to degrees and radians for sine, cosine and tangent functions.
Angle in Degrees 0 30 45 60 90 180 270 360
Angle in Radians 0 π/6 π/4 π/3 π/2 π 3π/2 2π
Sin 0 1/2 1/√2 √3/2 1 0 -1 0
Cos 1 √3/2 1/√2 1/2 0 -1 0 1
Tan 0 1/√3 1 √3 ∞ 0 ∞ 0
Unit Circle in Trigonometry
It is possible to give the values of trigonometric ratios with respect to radians equivalent to degrees, in case of a unit circle, whose radius is equal to one. The radian for a unit circle is denoted by π. In the below figure, the angle values are represented in degrees instead of radians.
Cos 60 Degree graph
You have learned about cos 60 degrees value along with other degree’s values here now. Also, the derived values for sin and tan with respect to degrees and radians. In the same way, we can find the values for other trigonometric ratios like secant, cosecant and cotangent.
Let us see some example where we can use the value of cos 60 degrees.
Example 1: Find the value of cos 60° + sin 30°.
Solution:
cos 60° + sin 30°
= cos 60° + sin (90° – 60°)
= cos 60° + cos 60°
= (1/2) + (1/2)
= (1 + 1)/2
= 2/2
= 1
Alternatively, cos 60° + sin 30° = (1/2) + (1/2) = (1 + 1)/2 = 2/2 = 1
Example 2: Calculate: 2 sin 60° – 4 cos 60°
Solution:
We know that, sin 60° = √3/2 and cos 60° = 1/2
Thus, 2 sin 60° – 4 cos 60° = 2(√3/2) – 4(1/2)
= √3 – 2
therefore it 3/2
Step-by-step explanation: Peace Out.... Have a good day
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When is an equation true?
Answer: when the value on each side of the equal sign is the same
Step-by-step explanation: for example, 9=9 is a true equation. 5+4 = 9 is a true equation
Can anyone write the equation of the graph?
The equation of given graph is y = |x - 3| + 5.
The graph of a absolute or modulus function is a V- shape graph. The function of absolute is f(x) = |x|. The general form of absolute function is f(x)=a |x - h| + k. Where (h,k) is the vertex of graph.
Here, we can see that graph is in the form of V shape, so the function will be absolute function. Now, we have to find the vertex of graph.
As seen from the graph the minimum point on the graph is located at the point (3, 5) and the value of a should be 1.
So, by putting the value of vertex in general equation we get the equation of the graph,
y = |x - 3| + 5
Therefore, the equation of given graph is y = |x - 3| + 5.
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what is 4x multipied by 7y
Answer:
Step-by-step explanation:
28xy
The normal price of a train ticket from Ashford to London is £34.20
Ross gets 1/3
off the price of his train ticket
Work out how much Ross pays for his ticket.
guys please help lol
Answer:
£22.80
Step-by-step explanation:
To work out how much Ross has to pay for his ticket, you first need to calculate how much the 1/3 of the full price is.
To do this, you divide the 34.20 by 3.
34.2 / 3 = 11.4
So Ross gets a discount of £11.40
To work out the price, that Ross has to pay, we substract the discount from the normal price:
34.2 - 11.4 = 22.8
So Ross pays £22.80 for his ticket.
