Suppose a certain baseball diamond is a square 60 feet on a side. The pitching rubber is located 40.5 feet from home plate on a line joining home plate and second
base.
(a) How far is it from the pitching rubber to first base?
(b) How far is it from the pitching rubber to second base?
(c) If a pitcher faces home plate, through what angle does he need to turn to face first base?
(a) The distance from the pitching rubber to first base is about feet.
(Round to two decimal places as needed.)
(b) The distance from the pitching rubber to second base is about feet.
(Round to two decimal places as needed.)
(c) He needs to turn about to his left.
(Round to one decimal place as needed.)
Answer: 41.7 feet from pitcher to 1st
13.2 feet from pitcher to 2nd
58 degrees to turn from home to 1st
distance from pitcher to the line from home to 1st is 57.5(sin45) = 57.5(.707) = 40.66
construct a right triangle with legs 40.66 and 50-40.66 = 9.34. then sum the legs' squares, and take the square root to get 41.72 feet
distance from home to 2nd = hypotenuse of a right triangle with sides 50 and 50, and angle of 45 degrees
50^2 + 50^2 = 2(2500) = 5000. sqr5000= 70.71, subtract 57.5. 70.71-57.5= 13.21 feet from pitcher to 2nd
Step-by-step explanation:
Determine whether each number is an integer, a rational number that is not an integral or an irrational number
The integers are 3√25, -185/5, rational = -1/4, 0.75, 3√25, -185/5, 4√8, irrational = √13,
An integer is the number zero (0), a positive natural number (1, 2, 3, etc.) or a negative integer with a minus sign.
A rational number is any number that can be written as a fraction, where both the numerator na demoninator that is the top and the bottom number are integers, and the denominator is cannot be zero
An irrational number is a type of real number which cannot be represented as a simple fraction.
A integer can always be a rational number but vice versa is not true.
Integer = 3√25 = 3x5 = 15
-185/5 = -37
rational = -1/4, 0.75, 3√25, -185/5, 4√8
irrational = √13,
Therefore, the integers are 3√25, -185/5, rational = -1/4, 0.75, 3√25, -185/5, 4√8, irrational = √13,
To learn more about rational numbers refer here
https://brainly.com/question/20400557
#SPJ1
please help me with this
The inequality shown on the number line is -3 < x ≤ 2
Inequality means when the two values that are not equal is defined by inequalities. Inequality means unequal.
When two values are not equal we will greater than or less than sign .
" < " means less than
" >" means greater than
"≤ " means less than and equal to
"≥ " means greater than and equal to
(a) Inequality -4 < n ≤ 5
here , -4 is not included so, the Number line starts from -3
5 is included so, number line will end on 5
(b) The number line shows ,
line is starting from -3 but the dot is not filled means it is not included
The line ends at 2 so,
Inequality is -3 < n ≤ 2
To know more about Inequality here
https://brainly.com/question/11612965
#SPJ1
graph the system of inequalities shown i need this quick
x>1
y>x
Answer:
Graph
Step-by-step explanation:
graph the line x=1 (vertical line passing through point (1,0))with a dotted line and shade everything to the right of the line. Then graph the line y=x (line with slope 1 passing through origin) with a dotted line, shading everything above the line.
Many bank accounts never go below zero. But some banks will allow a negative balance, at least for a short time, called an overdraft. It means someone has taken out, or 'drafted', more money than was in the account to begin with. Madeline's account went into overdraft. To get back to a positive balance, she deposited mone at a steady rate of $29.06 per week. After 8 weeks, she had $190.69 in the account. What was the balance when the account went into overdraft?
Answer:
-41.79
Madeline was overdrawn $41.79.
Step-by-step explanation:
If she deposited $29.06 a week for 8 weeks, she put
8 × 29.06
= 232.48
$232.48 into her account. But they're saying she now has only $190.69. Some of the money went to payback the negative balance she had.
Balance+232.48=190.69
Balance=190.69-232.48
Balance = -41.79
Madeline had a negative balance of $41.79.
Which expression represents the phrase? “The product of 8 and the quotient of 6 and and w.”
Answer:
B
Step-by-step explanation:
product means multiplication and quotient is division , then
product of 8 and the quotient of 6 and w is
8 ([tex]\frac{6}{w}[/tex] )
Write an equation in point-slope form that passes through (-4, -6) and is parallel to y= -7/2x+6. I'm stuck, please help.
Answer:
y= -7/2x-20
Step-by-step explanation:
parallel line so same slope
the equation given is in y=mx+b form so take out m:
m= -7/2
now input the coordinates and slope(m) given into y=mx+b to find b:
-6=-7/2(-4)+b
-6=28/2+b
-6=14+b
-6-14=b
b=-20
now write equation using slope(m) and y intercept(b)
y= -7/2x-20
Please mark as brainliesttt
The equation in point-slope pass through the given point will be y = -7/2x-20
What is an equation?Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
The same slope due to a parallel line,
Take away m from the above equation since it is in the y = mx+b form:
m= -7/2
Now, enter the given coordinates and slope(m) into y=mx+b to determine b:
-6 =-7/2 (-4) + b
-6 = 28/2 + b
-6 = 14 + b
b = -20
Slope(m) and y-intercept are now used to create an equation (b),
y = -7/2x-20
To know more about equation:
https://brainly.com/question/14686792
#SPJ2
8.7+x/1.1 = 7 solve for x
The solution of this Algebraic Equation is -1.0
What is an Algebraic Equation?
An algebraic equation is a mathematical statement which establishes two expressions equal to each other. An algebraic equation is generally composed of a variable, coefficients, and constants.
Solution:
According to the question,
the algebraic equation given is,
(8.7 + x)/1.1 = 7
By cross multiplying
8.7 + x = 7.7
x = -1.0
To learn more about Algebraic Equation from the given link
https://brainly.com/question/4344214
#SPJ1
8.54÷0.35= what the answer
The required solution is 24.4 to the given numerical expression 8.54 ÷ 0.35.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation.
The numerical expression is given in the question as:
8.54 ÷ 0.35
We have to determine the solution to the given expression
As per the question,
8.54 ÷ 0.35
8.54 / 0.35
(854/100) / (35/100)
Reciprocal the terms of numerator
854/100 × 100/35
854/35
Apply the division operation to get the solution
24.4
Thus, the required solution is 24.4 to the given numerical expression.
To learn more about the division operation click here :
brainly.com/question/25870256
#SPJ1
What is the length of AB
14
51
28
20
Answer:
51
Step-by-step explanation:
The segments are indicated to be congruent.
[tex]3x+9=5x-19 \\ \\ 9=2x-19 \\ \\ 2x=28 \\ \\ x=14 \\ \\ \implies AB=3(14)+9=51[/tex]
3x + 9 = 5x - 19
+ 19 + 19
3x +28 = 5x
- 3x -3x
28 = 2x
÷2 ÷2
14 = x
3x + 9
= 3(14) + 9
= 42 + 9
= 51You are given that a conditional is false and its hypothesis true. Determine whether the conclusion is true or false.
Answer:
The conclusion is false.
Step-by-step explanation:
If the conclusion is false, then the whole conditional is false even if the hypothesis is true.
Choose the expression that is equivalent to 1/4 x 12
Answer:
4%12
Step-by-step explanation:
Write the equation in standard form using integers
(no fractions or decimals): y= -2/3 x-1
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex]y=-\cfrac{2}{3}x-1\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y)=3\left( -\cfrac{2}{3}x-1 \right)} \\\\\\ 3y=-2x-3\implies {\Large \begin{array}{llll} 2x+3y=-3 \end{array}}[/tex]
Multiply (4.21 x 10-9) (7.8 x 1015). Write the final answer in scientific notation.
O 3.2838 x 107
O 32.838 x 106
O3.2838 x 10-134
O 32.838 x 10-135
4.21 x 10-9) (7.8 x 1015) = 32.838 * 10^6" ; the correct option is second.
What is multiplication ? In mathematics, multiplication is a way of finding the product of two or more numbers. This is one of the basic arithmetic operations that we use in our daily life. The main application can be seen in the multiplication table. In arithmetic, multiplication of two numbers represents the repeated addition of one number to another. These numbers include integers, natural numbers, whole numbers, fractions, and so on. Multiplying m by n means that m is added to itself n times, or vice versa. Multiplication in mathematics (denoted by an 'x') is an arithmetic operation separate from addition, subtraction, and division. Elementary school students learn the four arithmetic operations on their own and learn how to solve multiplication problems quickly and easily. Multiplication is the process of taking the product of two or more numbers. Multiplication of numbers such as 'a' and 'b' is given as 'a' multiplied by 'b'. In mathematics, the basic description of multiplication is the repeated addition of one number to another. Multiplying single-digit numbers is easy. However, multiplying numbers with two or more digits is a difficult and time-consuming task. Numbers can be multiplied in any order. (3x4 = 4x3)If you want to multiply the number by a multiple of 10, enter the number of zeros equal to the multiple of 10 next to the multiplier (for example, 6 x 100 = 600).When multiplying three numbers, multiply by the smaller number first to do the math quickly, then multiply by the third number.If the multiplication involves numbers with two or three digits, write those numbers in extended form and then multiply. (for example.:45 × 9 = (40 + 5) × 9 = 40 × 9 + 5 × 9 = 360 + 45 = 405)Calculation4.21 * 10 ^ -9 * 7.8 * 10 ^ 15 = 32.838 * 10^6
so the correct option is second
learn more about multiplication here :
brainly.com/question/5992872
#SPJ1
George wrote an integer. The opposite of George’s integer is -53. Which of these statements about George’s integer must be true?
I. The integer is 53.
II. The integer has an absolute value of -53.
III. The integer is -53.
IV. The integer has an absolute value of 53.
Answer
A
I and II
B
II and IV
C
II and III
D
I and IV NEED EXPLAINATION PLS
The George's integer must be true for option D)I and IV.
What is integer?
A full number (not a fraction) that can be positive, negative, or zero is called an integer . -5, 1, 5, 8, 97, and 3, 043 are some examples of integers. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers. Integer, which means full or whole in Latin, is the root of the English term integer. A particular category of numbers called integers includes zero, positive numbers, and negative numbers. All whole numbers, both negative and positive, and 0 are considered integers.
Here the opposite of George integer is -53.
We know that opposite value of x is -x.
Then George integer is 53.
George integer must be true for The given options I. the integer is 53 and IV.The integer has absolute value of 53.
Therefore the correct option is D) I and IV.
To learn more about integer refer the below link
https://brainly.com/question/13723636
#SPJ9
prime factorization for gcf and lcm for 25 and 60.
The gcf of 25 and 60 is 5
the lcm of 25 and 60 is 300
What is prime factorization?The process of determining which prime numbers combine to form the original number is known as prime factorization.
Prime factorization of 25 = 5 * 5
Prime factorization of 60 = 2 × 2 × 3 × 5
the greatest common factor, gcf of 25 and 60 is 5
The lowest common multiple, lcm of 25 and 60
= 2 * 2 * 3 * 5 * 5
= 300
Learn more about prime factorization here:
https://brainly.com/question/29362964
#SPJ1
which expression is equivalent to -24-12w
Answer:
Simplest form = -w - 2
Step-by-step explanation:
Given expression,
→ -24 - 12w
→ -12w - 24
Simplifying the expression,
→ -12w - 24
→ (-12w - 24)/12
→ -w - 2
Hence, the answer is -w -2.
an airplane flying with the wind can cover 560 miles in 2 hours. the return trip against the wind takes 2 1 2 hours. what is the speed of the plane? the speed of the plane is miles per hour. what is the speed of the air? the wind's speed is miles per hour.
The speed of the plane is 252 miles per hour and the speed of the wind is 28 miles per hour .
In the question ,
it is given that ,
the airplane covers the distance of 560 miles in 2 hours with the wind,
So , the speed of the airplane with the wind is 560/2 = 280 miles per hour
also given that
airplane covers the distance of 560 miles in 2.5 hours against the wind ,
So , the speed of the plane with the wind = 560/2.5 = 224 miles per hour .
let the speed of the airplane be "a" miles per hour ,
and let the speed of the wind be "b" miles per hour ,
So , equation of speed with the wind is denoted by
a + b = 280
and the equation of speed against the wind is denoted by
a - b = 224
Adding both the equations , we get
2a = 504
a = 504/2
a = 252 miles per hour
and b = 280 - 252 = 28 miles per hour .
Therefore , The speed of the plane is 252 miles per hour and the speed of the wind is 28 miles per hour .
Learn more about Speed here
https://brainly.com/question/19064729
#SPJ4
need help with this one
Number of solutions for the given linear quadratic equation y = x² and
y = 2x+ b is equal to 2.
b. As we change the value of b solution of the linear system of equation get modify. For example b = 0 it passes through origin.
As given in the question,
Given linear quadratic equations are:
y = x² and
y = 2x+ b
⇒ x² = 2x + b
⇒ x² -2x -b = 0
Number of solutions depends on :
Discriminant 'D' = b² -4ac
Here a = 1 , b = -2 , c= -b
D = (-2)² - 4(1)(-b)
= 4 + 4b
If D > 0 there are two real solutions.
If D = 0 there is only one solution.
If D < 0 there is no solution.
Value of D depends on the value of 'b' .
Linear quadratic equation has two solutions if D > 0.
Graph is attached for the given quadratic equations.
Therefore, number of solutions for the given linear quadratic equation y = x² and y = 2x+ b is equal to 2.
b. As we change the value of b solution of the linear system of equation get modify. For example b = 0 it passes through origin.
Learn more about linear quadratic equation here
brainly.com/question/12788590
#SPJ1
a recent survey found that 70% of all adults wear sunglasses for driving. in a random sample of 10 adults, what is the probability that at least five wear sunglasses?
The probability that at least five wear sunglasses is 0.9464
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
In a random sample of 10 adults, the probability that at least five wear sunglasses
P(X ≥ 5) = P(X = 5) + P(X = 6 ) + P(X=7) + P(X=8) + P(X=9) + P(X=10)
P(X ≥ 5) = 10[tex]C_{5}[/tex] × [tex](0.7)^{5}[/tex]×[tex](0.3)^{5}[/tex] + 10[tex]C_{6}[/tex]×[tex](0.7)^{6}[/tex]× [tex](0.3)^{4}[/tex]+ 10[tex]C_{7}[/tex]×[tex](0.7)^{7}[/tex]×[tex](0.3)^{3}[/tex] + 10[tex]C_{8}[/tex]× [tex](0.7)^{8}[/tex]×[tex](0.3)^{2}[/tex] +10[tex]C_{9}[/tex] ×[tex](0.7)^{9}[/tex]×[tex](0.3)^{1}[/tex]+10[tex]C_{10}[/tex]×[tex](0.7)^{10}[/tex]×[tex](0.3)^{0}[/tex]
P(X ≥ 5) = 0.9464
The probability that at least five wear sunglasses is 0.9464
To learn more about probability:
https://brainly.com/question/11234923
#SPJ4
Which of the following people likely pays the LEAST for health care?
a. Tanya, who has a Bronze level plan and goes to the doctor for an annual exam once all year
b. Alfred, who has a Bronze level plan and uses it for a few doctor appointments, an X-ray, and to fill
monthly prescriptions
c.
Marty, who does not sign up for health insurance and then has a 4-week hospital stay because he gets
pneumonia
d. Caroline, who has a Silver level plan and uses it frequently in the year, because she's pregnant and due
have a baby
Tanya, who has a Bronze level plan and only goes to the doctor once a year for an annual exam, is likely to pay the least for healthcare. The correct option is A.
What is health care?Health care refers to the maintenance or improvement of an individual's physical or mental health through the prevention, diagnosis, and treatment of illness, injury, or disease. It encompasses a range of services provided by healthcare professionals.
Based on the information provided, Tanya, who has a Bronze level plan and only goes to the doctor once a year for an annual exam, is likely to pay the least for healthcare.
Bronze level plans typically have lower monthly premiums but higher out-of-pocket costs for healthcare services, such as copays, deductibles, and coinsurance.
Since Tanya only goes to the doctor once a year, she is unlikely to meet her deductible or incur significant out-of-pocket costs.
In contrast, options B, C, and D involve more frequent or more serious healthcare needs, which would likely result in higher out-of-pocket costs for healthcare services.
Thus, the correct option is A.
For more details regarding healthcare, visit:
https://brainly.com/question/12881855
#SPJ2
The volume of a rectangular prism is represented by the function x3 9x2 6x − 16. the length of the box is x 2, while the height is x 8. find the expression representing the width of the box. x − 4 x − 1 x 1 x 4
The expression that represents the width of the box is (x - 1) , the correct option is (b) .
In the question ,
it is given that ,
the Volume of the rectangular prism is = x³ + 9x² + 6x – 16
the measure of the length of the box = x+2
the measure of the height of the box = x+8
formula for Volume of Prism is
Volume = l × w × h
where l = length of the prism,
w = width of the prism and
h = height of the prism.
Substituting the values ,
we get ,
x³ [tex]+[/tex] 9x² [tex]+[/tex] 6x – 16 [tex]=[/tex] (x [tex]+[/tex] 2) * (x [tex]+[/tex] 8) * width
On dividing the equation (x³ + 9x² + 6x – 16) with (x+2)
and then dividing the result with (x+8) , we get
width = (x-1) .
Therefore , The expression that represents the width of the box is (x - 1) , the correct option is (b) .
The given question is incomplete , the complete question is
The volume of a rectangular prism is represented by the function x³ + 9x² + 6x – 16. The length of the box is x + 2 while the height is x + 8. Find the expression representing the width of the box
(a) x - 4
(b) x - 1
(c) x + 1
(d) x + 4
Learn more about Volume here
https://brainly.com/question/1583874
#SPJ4
Answer:
B
Step-by-step explanation:
Asked my teacher to help me.
The community center has a pottery class each month each student pays $15 for the class and $27 for materials this month the pottery class brought in a total of $715 how many students are in the class the month?
Answer:17
Step-by-step explanation:
please help me!!!!!!!!!!1
The value of x for the given equation is -20 .
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
(5/3)x+(1/3)x=13(1/3)+(8/3)x
Solve equation, to find the value of x,
(5/3+1/3)x=13(1/3)+(8/3)x
-13(1/3)=(8/3)x-(5/3+1/3)x
-40/3=(8/3-2)x
1.(-40/3)=1.(2/3)x
-20=x
To know more about Equation on:
https://brainly.com/question/187506
#SPJ1
pls help!
Simplify the expression to a + bi form:
√4 + √−45 + √49 + √−45
Answer: 9+6i√5
Step-by-step explanation:
√4 + √−45 + √49 + √−45
2 + √45i + 7 + √45i
9 + 3i√5 + 3i√5
9+6i√5
Estimate a 25% tip on a bill of 68.37$ by first rounding the bill amount to the nearest ten dollars.
Answer:
20 dollar tip (rounded) assuming the bill is 68.37
Step-by-step explanation:
just multiply 68.37 by 0.25, and you get 17.09 or 20 dollars rounded to TENS place.
SOLVES FOR 50 POINTS AND BARINLISTEST
Answer:
(-2, 3 1/3)
2nd one
Step-by-step explanation:
2/3*-3=-2 so x=-2
2/3*5=10/3= 3 1/3 so y= 3 1/3
(-2, 3 1/3)
5 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a 3? Express your answer as a fraction or a decimal number rounded to four decimal places.
The probability that at least one of the cards drawn is a 3 is 1/5 0r 0.2000.
What is probability?
Probability shows the likelihood of an event happening. It can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1. It is less than '1' when it is not likely to occur. i.e P< 1
Probability P=no. outcomes/total no. of the possible outcomes
From the question;
No. of total no of cards =5
The probability the card drawn is a 3 =1/5
=0.2000
Therefore the probability that at least one of the cards drawn is a 3 is 1/5 0r 0.2000.
Learn more about probability on
https://brainly.com/question/23704607
#SPJ1
lisa receives a salarry of rs 9500 per month plus a commision of 10 % on all sales. For te month of December, she earns rs 14000. find her total sales in december
Total earning = Salary + 10% of sales
According to question, we have
14000 = 9500 + 10% of sales
4500 = 0.1 sales
sales = 4500*10 = 45000
So, her total sales was Rs 45000
Find the value of the expression (2x − 12) + (xy-10) for x = 8 and y = 2.
-
O-8
O 6
O-10
02o
The required value of the expression (2x − 12) + (1/2 xy - 10) for x = 8 and y = 2 is 2. Option D is correct.
First, let us understand the algebraic expression and how is it formed:
A multitude of strategies is used to build algebraic expressions utilizing variables and constants. It is a term-based mathematical expression that comprises variables, constants, and algebraic operations such as addition, subtraction, and so on.
We are given:
(2x − 12) + (1/2 xy - 10)
We need to find the value of the given expression for x = 8 and y = 2.
Substitute the values of x and y in the given expression, we will get;
(2 * 8 − 12) + (1/2 * 8 * 2 - 10)
= (16 − 12) + (8 - 10)
= 4 + (-2)
= 4 - 2
= 2
So, the obtained value is 2.
Thus, the required value of the expression (2x − 12) + (1/2 xy - 10) for x = 8 and y = 2 is 2. Option D is correct.
To learn more about algebraic expression visit:
brainly.com/question/28884894
#SPJ1